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Orthogonoid spaceship -- completed!

For discussion of specific patterns or specific families of patterns, both newly-discovered and well-known.

Re: Orthogonoid working notes

Postby dvgrn » May 24th, 2016, 11:47 am

simsim314 wrote:A more practical question: do we have some block->SL recipes list? Preferably limited list, of say 10 good recipes per SL per orientation? ( + we need block moving list)

Not sure how to handle this exactly. I do have a P2 block-move table up to 9 gliders, and also about a quarter of million block-to-constellation recipes generated from the block-move recipes.

I've often used the block-to-constellation table to find ways to build two objects simultaneously -- usually a catalyst object plus a block in exactly the right place to start the next construction. Sometimes I sort the table by the number of gliders, and sometimes by the total width of the slow-salvo glider lanes (figuring that recipes with all lanes near each other will be cheaper to construct than recipes that jump around over a wide range -- not always true, but maybe slightly true on average).

There are all sorts of difficult optimization problems hiding here. Really, of all the possible slow salvos that can build Constellation X, we want the one that can be coded by the shortest amount of data on the data tape. That depends not only on the specific elbow-op library being used, but also on which Constellation W was constructed previously, and which Constellation Y will be constructed next (the elbow's starting and ending positions both matter).

So... ignoring all those problems, it's pretty easy to pick out a couple dozen of the shortest block-to-object recipes, probably choosing recipes that have reaction envelopes as different from each other as possible, and recipes that have the constructed object right on the edge of the reaction envelope (back, left side, and also right side for asymmetrical objects).

You don't really want a block-to-object library, though, you want block-to-(object-plus-block), or more generally target-to-(object-plus-target). See this post for example, for an explanation of some of the lookup shortcuts I used in the linear replicator.

Recently simeks' search utility has been re-doing the search to produce something like that quarter-million-recipe library, much more thoroughly (my source of data wasn't an exhaustive search) -- but starting with a blinker instead of a block, at least sometimes. That was back in January; I don't know if there's a complete library available yet for different kinds and orientations of Spartan still lifes.

Blinkers are good as targets, because blocks have only one reasonable next step, a honeyfarm conversion, plus the two block pulls. Blinkers have a lot more branches right at the root of their search tree, and as long as you can build P2-slow salvos, and the constellation you're building is P1, then it seems like it will be significantly more efficient to use blinkers as the persistent target "hand" objects.

Or blinkers might just be one possible target object out of maybe twenty -- e.g., blinker, block, honeyfarm, traffic light, tub, pond, beehive, ship, and three different orientations each of boats, loaves and long boats. That would mean 17 different lookup tables depending on the target object, or 22 if we just duplicate the tables for mirror-image orientations.

-- Could maybe add toads to the list, and maybe a few other common pseudo-objects and small constellations like bi-blocks and half-blockades, but after that it seems like additional objects would be so rare that the tables would never see any use.

Maybe we could start with just block-to-(object-plus-block) and blinker-to-(object-plus-blinker) tables, plus a blinker-move table, and compile an Orthogonoid once with each library to see if blinkers are really an improvement. Then maybe we'd add block-to-blinker and blinker-to-block movement tables, and work up from there.

simsim314 wrote: I know you post the recipes time after time in the discussions, maybe we could have a thread with all recipes on the first page like we have with Conduits? Maybe we need similiar thread, something like - the hunt for the optimal slow salvo compiler?

Yeah, whoever has a script or a good collection of data to share first, should probably start that thread.
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Re: Orthogonoid working notes

Postby chris_c » May 24th, 2016, 5:52 pm

Here is a bit of an improvement to the "Stage 1" design. Maybe it is possible to make the eater directly from the construction elbow to reduce the cost further.

x = 207, y = 265, rule = LifeHistory
129.2A$129.2A3$126.2A$126.A.A$124.A.A.3A$124.2A5.A$130.2A82$159.A$
158.A.A$158.A2.A$159.2A2$118.A$116.3A37.2A$115.A40.A.A$115.2A40.A2$
148.2A$147.A2.A15.2A$148.A.A15.A.A$119.2A5.2A21.A16.A$119.2A5.2A2$
122.2A$122.2A5$101.2A.2A$100.A5.A$95.2A2.A6.A$95.2A3.A3.3A$101.A8$
120.A$119.A.A$120.2A8$92.2A$93.A$90.3A$90.A$205.A$204.A.A$204.2A$109.
2A$109.2A4$142.A$142.3A$145.A14.A$144.2A12.3A$157.A$157.2A3$156.2A$
137.2A17.2A$137.2A4$100.2A$100.2A$106.2A32.2A$106.2A33.A$138.3A$138.A
$104.2A37.2A$104.2A5.2A31.A$111.2A28.3A$141.A5$160.2A$160.A.A$162.A$
162.2A6$151.2A$142.2A7.2A$143.A$102.A40.A.A$102.3A33.2A4.2A$89.2A3.2A
9.A17.A15.A20.2A$89.2A3.2A8.2A15.3A15.A.A18.A$120.A19.2A16.A.A$120.2A
36.2A$82.2A$83.A$83.A.A$84.2A2$123.2A$123.2A4$87.2A63.2A$88.A63.2A2.
2A$85.3A28.2A38.A.A$85.A31.A15.2A23.A$117.A.A14.A23.2A$118.2A11.3A$
131.A4$100.2A$100.2A$92.2A$93.A$90.3A$90.A2$91.A$90.A.A$90.A.A$88.3A.
2A$87.A$88.3A.2A$90.A.2A2$100.2A$100.2A7.2A$109.A$107.A.A$107.2A4$87.
2A$87.2A5$103.A$102.A.A$102.A.A$103.A$104.3A$106.A7$2.A119.A$A3.A115.
A3.A$5.A70.5A44.A$A4.A69.A4.A39.A4.A3.2A$.5A74.A40.5A3.2A$75.A3.A$77.
A$126.2A$126.A.A$124.A.A.3A$124.2A5.A$130.2A!
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Re: Orthogonoid working notes

Postby dvgrn » May 24th, 2016, 6:54 pm

chris_c wrote:Here is a bit of an improvement to the "Stage 1" design. Maybe it is possible to make the eater directly from the construction elbow to reduce the cost further.

That's funny -- I thought of the same thing today, but for the Stage 0 design. Here's a draft stable Orthogonoid that uses Extrementhusiast's 22-lane-clearance eater seed.

Stage-0 Orthogonoid-371:
x = 113, y = 245, rule = LifeHistory
70.2AB$69.B2A5B2.B3.3B$69.12B.6B21.B$69.19B20.2B$68.9B2A10B18.3B$68.
9BABA12B14.4B$67.11BA13B13.4B$67.26B11.4B$66.3B3A21B10.4B$64.28B10.4B
$63.27B11.4B$63.26B11.4B$64.25B10.4B$67.24B7.4B$67.25B5.4B$72.21B3.4B
$71.22B2.4B$72.26B$72.25B$73.6B2.15B$82.10B.4B$84.B.6B2.4B$71.2A11.6B
2D3.4B$70.B2AB11.5BD5.4B$64.B6.2B12.3BDBD3.BC.4B$63.3B4.2B14.2B2D3.CB
CB.4B$59.14B14.2B5.2C2B.4B$59.14B22.4B.4B$59.17B5.B14.4B.4B$58.25B14.
4B.4B$56.29B13.4B.4B$55.30B.B12.4B.4B$54.32B14.4B.4B$53.33B14.10B$52.
4B3.26B2A12.7B2C3B$51.4B7.16B.B4.BA.A10.4B.2BCBC3BC$50.4B9.2B.10B11.A
9.4B2.3BC3BCBC$49.4B13.9B12.2A7.4B4.6B2C$48.4B15.11B17.4B6.2B.B$47.4B
16.12B15.4B$46.4B17.12B14.4B$45.4B19.11B13.4B$44.4B18.4B.4B3DB12.4B$
43.4B19.2A4.4BD2B11.4B$42.4B21.A4.2B3D2B10.4B$41.4B19.3A6.6B9.4B$40.
4B20.A8.7B7.4B$39.4B30.8B5.4B$33.B4.4B32.8B3.4B$31.4B2.4B33.7B4.3B$
30.10B33.6B3.2E.2B$29.2B2D6B.3B30.7B2.E.EB$28.2BD2BD10B30.6B4.E$12.2B
13.4B2D9BA2B29.6B4.2EB$5.B.B.B.3B.D.B.B.B.B.16BABA30.6B6.2B$5.8BD3BD
24B2A29.8B5.3B$5.7BD30B29.8B6.4B$5.7BD4BD23B31.9B6.4B$5.7B5D25B30.9B
7.4B$5.37B29.10B8.4B$6.B.B.B.B.B.B.B.B.B.B.16B29.3B2A5B9.4B$28.14B28.
4B2A5B10.4B$28.13B29.11B11.4B$28.11B29.A7BD4B12.4B$27.13B26.3A2.4B3DB
15.4B$26.15B24.A6.2B2D2BD16.4B$25.16B24.2A6.6B17.4B$24.17B32.7B17.4B$
25.16B31.7B5.2A12.4B$26.13B33.8B3.A.A13.4B$26.5B2A2B37.8B3.A$28.3B2A
2B37.9B.2A$28.8B35.11B$27.3B3D2B35.12B$27.4BD3B35.12B$27.2B3D2B29.2A
6.10B$27.7B30.A7.11B$28.6B7.A22.A.AB.14B$28.6B6.A.A22.2AB.13B2A$29.5B
6.A.A24.15B2A$29.6B4.2A.3A21.15B.B$28.6B6.B4.A21.14B$28.7B3.B2AB3A20.
2AB.11B$29.8B.B2A.A21.A.AB3.9B$29.10B25.A8.8B$28.3B2A6B24.2A9.7B$22.
2A5.2B2A6B32.11B$23.A5.10B31.12B$23.A.AB2.11B30.12B$24.2AB.12B30.11B$
17.2A7.15B29.B3D4B.4B$16.B2A2B5.16B28.2BD4B4.2A$17.4B5.16B.2B25.2B3D
2B4.A$18.3B5.18B2A24.6B6.3A$3.2A5.3B4.3B5.17B.B2A23.7B8.A$4.A4.4B2.7B
2.4B2.8B.4B.B23.8B$4.A.AB.18B4.7B29.8B$5.2AB.17B5.6B30.8B$7.18B6.4B
30.2AB2.6B$7.18B4.A3B31.A.AB.7B$6.18B4.A.AB32.A4.6B$6.18B4.A.A32.2A4.
6B$6.18B5.A39.6B$6.18B2.3A39.8B$7.16B3.A42.8B$5.18B45.9B$3.A.2A4.12B
45.9B$.3AB2A4.13B44.10B$A4.B4.15B43.5B2A3B$.3A.2A3.16B42.5B2A4B3.2A$
3.A.A4.17B41.11B3.A$3.A.A4.16B42.4BD7BA.A$4.A7.13B45.B3D4B2.2A$16.2B
2A5B45.D2B2D2B$16.2B2A3B47.5B$15.8B39.2A5.6B$16.2B3D3B39.A6.6B$16.3BD
4B39.A.AB2.8B$17.2B3D2B40.2AB2.9B$17.7B42.12B$9.A7.6B43.12B$8.A.A6.6B
43.10B.B2A$8.A.A6.5B45.8B2.BA.A$6.3A.2A4.6B44.8B6.A$5.A4.B6.6B44.8B5.
2A$6.3AB2AB3.7B45.7B$8.A.2AB.8B43.11B$12.10B42.12B$12.6B2A3B41.12B$
12.6B2A2B5.2A35.11B$12.10B5.A36.B3D4B.4B$11.11B2.BA.A36.2BD4B4.2A$11.
12B.B2A37.2B3D2B4.A$10.15B39.7B5.3A$9.16B38.7B8.A$6.2B.16B37.8B$5.2A
18B36.8B$5.2AB.17B35.8B$6.B.4B.8B2.4B32.2AB2.6B$13.7B4.4B30.A.AB.7B$
14.6B5.4B29.A4.6B$16.4B6.4B27.2A4.6B$18.3BA5.4B32.6B$19.BA.A5.4B30.8B
$20.A.A6.4B30.8B$21.A8.4B28.9B$22.3A6.4B27.9B$24.A7.4B26.10B$62.5B2A
3B$62.5B2A4B3.2A$62.11B3.A$62.4BD7BA.A$64.B3D4B2.2A$64.D2B2D2B$64.5B$
64.5B$41.4B18.7B$29.2A3.2A6.4B18.6B$28.B2AB.B2AB6.4B17.5B$29.2B2.3B3.
B4.4B13.8B$30.3B.3B.4B4.3B10.10B$22.2A5.7B.13B8.12B$23.A5.23B6.13B$
23.A.AB.19B.8B2.12B$24.2AB.29B.13B$26.45B$26.33BD13B$26.33B2D9BA4B$
27.33B2D7BABA4B$29.31BD8BABA4B$27.32BD10BA4B$27.2A3.25B4.B.2B3.5B$28.
A3.20B4.B3.3B7.B$25.3A6.15B7.2A2.B2AB5.3B$25.A8.11B12.A3.2A6.B2AB$33.
13B8.3A13.2A$32.15B7.A$32.16B$32.17B$32.16B$34.13B$33.4B.2B2A5B$32.4B
2.2B2A3B$31.B2AB2.8B$31.2BA4.2B3D3B$30.3A5.3BD4B$30.AB7.2B3D2B$39.7B$
31.A7.6B$30.A.A6.6B$30.A.A6.5B$28.3A.2A4.6B$27.A4.B.B4.6B$28.3AB2A2B
2.7B$30.A.2A10B$34.10B$34.6B2A3B$34.6B2A2B5.2A$34.10B5.A$33.11B2.BA.A
$33.7B3A2B.B2A$32.8BA6B$31.10BA5B$28.2B.16B$27.2A18B$27.2AB.17B$28.B.
4B.8B2.4B$35.7B4.4B$36.6B5.4B$38.4B6.4B$40.3BA5.4B$41.BA.A5.4B$42.A.A
6.4B$43.A8.4B$44.3A6.4B$46.A7.4B$55.4B$56.4B$57.4B$58.4B$59.4B$60.4B$
61.2B2A$62.BABA$63.A3B$64.4B9$4.B.C.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B
.B.B.B.B.B.B.B.B.B.B.B.D.B.B.B.5B$3.BC3BC53BD3BD12B$3.6BC57BD12B.B$3.
BC4BC52BD4BD13B2A$3.2B5C53B5D13B2A$3.76B2.B$3.B.B.B.B.B.B.B.B.B.B.B.B
.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B2.2B$77.B2A$78.A.A.
2A$76.A.A.2A.A$76.2A!

High clearance is generally good when you're trying to block a single-channel construction arm, but probably not really needed here. Both eaters can be adjusted as necessary, and the initial elbow objects can be built as far out from the glider-emitting circuit as needed to avoid any clearance problems.

This design reduces the number of eater2s by a factor of three from the last Stage-0 design, and cuts the population roughly in half, to 371 cells.

Something along these lines looks to me like a good first Orthogonoid blueprint. Once we have a half-decent Spartan constellation-to-slow-salvo compiler and a slow-salvo-to-single-channel compiler, there's relatively little work left to get to a working spaceship.

Mostly it's just a matter of tacking on a slow salvo that shoots down the previous replicator unit, and then cleanly destroys the destruction-arm elbow. I guess that last part is optional -- could shoot down the elbow the next time around... but it would probably be more expensive.

This is just the first circuit combination that worked, so I suspect the size and/or population can be cut down some more. There are three different lanes that can knock out that beehive from the northeast -- maybe more if a few catalysts are added up there -- and there are lots of fast Spartan conduits and Spartan H-to-Gs to try combining.

It would be nice to be able to knock out the beehive with a glider from the southwest or southeast, but it looks to me as if that can't be done with signals with 90-tick separation. Am I missing any good tricks there?
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Re: Orthogonoid working notes

Postby chris_c » May 24th, 2016, 7:19 pm

dvgrn wrote:That's funny -- I thought of the same thing today, but for the Stage 0 design. Here's a draft stable Orthogonoid that uses Extrementhusiast's 22-lane-clearance eater seed.


Oooh... that looks pretty good. I had a bit of a go at reducing the Stage 0 design but didn't get anything nearly as nice.

I have been hacking my elbow search code to see if I can make a "from the elbow" eater with the single channel design. Will post if anything good turns up.
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Re: Orthogonoid working notes

Postby dvgrn » May 24th, 2016, 10:15 pm

chris_c wrote:I have been hacking my elbow search code to see if I can make a "from the elbow" eater with the single channel design. Will post if anything good turns up.

It seems pretty much okay if the final reaction produces a fairly large amount of junk, as long as it catches gliders (and doesn't emit any). It should be fairly cheap to clean it up with the destruction arm in the next cycle.

Does anyone have working or nearly-working code that can produce good X-to-(Y-plus-Z) recipes -- something that a constellation-to-slow-salvo compiler could use? I can easily filter my 236,000 recipes to come up with a "starter kit" for block-to-(object-plus-block), but that collection came from truncating the P2 block-move table, not from an exhaustive search, so I'd kind of like to come up with a more complete library this time around.
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Re: Orthogonoid working notes

Postby chris_c » May 25th, 2016, 5:50 am

dvgrn wrote:It seems pretty much okay if the final reaction produces a fairly large amount of junk, as long as it catches gliders (and doesn't emit any). It should be fairly cheap to clean it up with the destruction arm in the next cycle.


I had some bugs in the search code so nothing to report yet.

dvgrn wrote:Does anyone have working or nearly-working code that can produce good X-to-(Y-plus-Z) recipes -- something that a constellation-to-slow-salvo compiler could use? I can easily filter my 236,000 recipes to come up with a "starter kit" for block-to-(object-plus-block), but that collection came from truncating the P2 block-move table, not from an exhaustive search, so I'd kind of like to come up with a more complete library this time around.


The closest thing I have is the code from here. I spent a bit of time modifying it just now. The code below starts from block and blinker and outputs a solution when the pattern has between 7 and 11 cells, has area greater than 16 and has at most 1 blinker. I imagine that simeks code you mentioned above will be many times faster... :)

import golly as g
from hashlib import sha256
from itertools import chain

#arbitrary numbers
MAX_GENERATIONS = 256
MAX_POPULATION = 40
MAX_GLIDERS = 3

#NE glider
GLIDER = g.parse('3o$2bo$bo!')

#put any ad-hoc patterns that you want to bombard with slow gliders here.
TARGET_PATTERNS = []#('known_splitter', 'bo$obo$b2o$5bo$4bobo$5bobo$6b2o!')]

#put simple targets here, along with rotational symmetry
SIMPLE_TARGETS = [
  ('block', '2o$2o!', 4),
  ('blinker', '3o$!', 4),
#  ('tub', 'bo$obo$bo!', 4),
#  ('boat', 'b2o$obo$bo!', 1),
#  ('hive', 'b2o$o2bo$b2o!', 2),
#  ('ship', 'b2o$obo$2o!', 2),
#  ('loaf', 'b2o$o2bo$bobo$2bo!', 1),
#  ('lboat', '2b2o$bobo$obo$bo!', 1),
#  ('pond', 'b2o$o2bo$o2bo$b2o!', 4),
# ('tlight', '4bo$4bo$4bo2$3o3b3o2$4bo$4bo$4bo!', 4),
# ('hfarm', '6bo$5bobo$5bobo$6bo2$b2o7b2o$o2bo5bo2bo$b2o7b2o2$6bo$5bobo$5bobo$6bo!', 4),
]

def get_pattern_variants(cells, symmetry):
  variants = []
  for t in range(0, 4, symmetry):
    variants.append(cells)
    cells = g.transform(cells, 0, 0, 0, -1, 1, 0)
  return variants

TARGETS = []
for name, pattern in TARGET_PATTERNS:
  cells = g.parse(pattern)
  p = len(cells) / 2
  TARGETS.append((name, cells, p))

for name, pattern, sym in SIMPLE_TARGETS:
  cells = g.parse(pattern)
  variants = get_pattern_variants(cells, sym)
  for i, v in enumerate(variants):
    p = len(v) / 2
    TARGETS.append((name+str(i), v, p))

def patterns_identical(cells1, cells2):
  if len(cells1) != len(cells2):
    return False
  if sum(cells1) != sum(cells2):
    return False
  return sorted(zip(cells1[::2], cells1[1::2])) == sorted(zip(cells2[::2], cells2[1::2]))

def get_pattern_period(cells):
  temp_cells = cells
  for p in range(0, 2):
    temp_cells = g.evolve(temp_cells, 1)
    if patterns_identical(cells, temp_cells):
      return p+1
  return None

def get_shooting_range(cells):

  min_d1 = max_d1 = cells[0] + cells[1]
  min_d2 = cells[0] - cells[1]

  for i in range(2, len(cells), 2):
    min_d1 = min(min_d1, cells[i] + cells[i+1])
    max_d1 = max(max_d1, cells[i] + cells[i+1])
    min_d2 = min(min_d2, cells[i] - cells[i+1])

  min_lane = min_d1 - 6
  max_lane = max_d1 + 3
  shift = 6 - min_d2 // 2

  return min_lane, max_lane, shift

def get_pattern_to_try(cells, lane, parity, offset=50):
  glider = g.transform(GLIDER, lane - lane // 2 - offset, lane // 2 + offset)
  if parity % 2:
    glider = g.evolve(glider, 1)
  return list(chain(cells, glider))

offset = 0

def display_solution(start, lanes, debug, last_cells):

  global offset

  cells = [c for n, c, _ in TARGETS if n == start][0]
  i = 100
  for lane in lanes:
    lane_num, parity = lane
    cells = get_pattern_to_try(cells, lane_num, parity, i)
    i += 100
  g.putcells(cells, 0, offset)
  for i, p in enumerate(debug):
    g.putcells(p, 100 + 100 * i, offset)
  g.putcells(last_cells, 100 + 100 * len(debug), offset)
  g.fit()
  g.update()
  g.show(' '.join(chain([str(start), str(len(lanes))], [str(lane) for lane in lanes])))
  offset += 400

# Detect all patterns of population between 7 and 11, area greater than 16
# and at most 2 unstable cells
def is_y_plus_z(cells):

    if len(cells) < 2 * 7 or len(cells) > 2 * 11:
        return False

    width  = max(cells[::2]) - min(cells[::2]) + 1
    height = max(cells[::2]) - min(cells[::2]) + 1

    if width * height <= 16:
        return False

    new_cells = g.evolve(cells, 1)
    new_cells = set(zip(new_cells[::2], new_cells[1::2]))

    unstable = 0
    for i in range(0, len(cells), 2):
        if (cells[i], cells[i+1]) not in new_cells:
            unstable += 1
   
    return unstable <= 2

randoms = []
for i in range(4096):
  randoms.append(int(sha256(str(i)).hexdigest()[:16], 16))

def to_hashable(cells):
  if not cells:
    return 0

  minx = min(cells[::2])
  miny = min(cells[1::2])

  hash = 0
  for i in range(0, len(cells), 2):
    hash ^= randoms[64 * ((cells[i] - minx) & 63) + ((cells[i+1] - miny) & 63)]

  return hash

def deltas(cells):
  return len(cells), sum(cells[::2]), sum(cells[1::2])


g.new('')

new_queue = []
for name, cells, _ in TARGETS:
  period = get_pattern_period(cells)
  new_queue.append( (name, [], cells, period, []) )

seen = set()

for n in range(MAX_GLIDERS):

  queue = new_queue
  new_queue = []

  count = 0

  for start, lanes, last, period, debug in queue:

    g.show(str((n+1,count,len(queue))))
    count += 1

    min_lane, max_lane, shift = get_shooting_range(last)

    for lane_num in range(min_lane, max_lane + 1):

      for parity in range(period):
       
        lane = (lane_num, parity)
        start_cells = get_pattern_to_try(last, lane[0], lane[1], shift)
        new_cells = g.evolve(start_cells, MAX_GENERATIONS)

        if not new_cells or len(new_cells) > 2 * MAX_POPULATION:
          continue

        new_period = get_pattern_period(new_cells)
        if new_period is None:
          continue

        new_hashable = to_hashable(new_cells)       

        if new_hashable in seen:
          continue

        seen.add(new_hashable)
        if new_period > 1:
          seen.add(to_hashable(g.evolve(new_cells, 1)))
       
        new_lanes = lanes + [lane]
        new_debug = debug + [start_cells]
         
        if is_y_plus_z(new_cells):
          display_solution(start, new_lanes, new_debug, new_cells)

        if n + 1 < MAX_GLIDERS:
          new_queue.append( (start, new_lanes, new_cells, new_period, new_debug) )


EDIT: I found a recipe for an eater in boat-bit making position (actually I found two but this one is cleaner). The minimum glider spacing is 94 ticks in the second pair.

#C e109 e94 o9999 e136 e9999 e9999 o104 e9999 e138 e121 e111 e9999 o9999
x = 1765, y = 1769, rule = LifeHistory
1763.2C$1763.2C76$1689.3A$1691.A$1690.A25$1662.2A$1663.2A$1662.A101$
1559.3A$1561.A$1560.A21$1536.2A$1535.A.A$1537.A104$1430.A$1430.2A$
1429.A.A159$1269.3A$1271.A$1270.A32$1235.3A$1237.A$1236.A94$1139.3A$
1141.A$1140.A128$1009.3A$1011.A$1010.A127$880.A$880.2A$879.A.A24$854.
A$854.2A$853.A.A103$749.3A$751.A$750.A128$619.3A$621.A$620.A32$585.2A
$584.A.A$586.A94$489.3A$491.A$490.A28$459.2A$460.2A$459.A98$359.3A$
361.A$360.A25$332.A$332.2A$331.A.A101$229.3A$231.A$230.A127$100.A$
100.2A$99.A.A78$20.3A$22.A$21.A8$10.3A$12.A$11.A8$3A$2.A$.A!
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Re: Orthogonoid working notes

Postby simeks » May 26th, 2016, 1:30 pm

dvgrn wrote:Maybe it is possible to make the eater directly from the construction elbow to reduce the cost further.

Here's a recipe for a clean eater (integral):
{109,255, 94,255,255,152,255, 90,255,117,255, 91,255,256,113,256,168,255, 90,255,135,255,255, 91,255,107, 0}

x = 1289, y = 1293, rule = LifeHistory
1287.2C$1287.2C4$1285.3A$1287.A$1286.A25$1258.2A$1259.2A$1258.A62$
1194.3A$1196.A$1195.A21$1171.2A$1170.A.A$1172.A62$1107.2A$1108.2A$
1107.A62$1043.3A$1045.A$1044.A36$1005.3A$1007.A$1006.A61$942.A$942.2A
$941.A.A21$919.2A$920.2A$919.A62$855.3A$857.A$856.A27$826.2A$827.2A$
826.A62$762.3A$764.A$763.A20$740.A$740.2A$739.A.A62$676.2A$675.A.A$
677.A62$612.2A$611.A.A$613.A26$584.A$584.2A$583.A.A62$520.A$520.2A$
519.A.A40$478.A$478.2A$477.A.A62$414.2A$413.A.A$415.A21$391.3A$393.A$
392.A61$328.A$328.2A$327.A.A32$294.2A$293.A.A$295.A62$230.2A$231.2A$
230.A62$166.3A$168.A$167.A20$144.A$144.2A$143.A.A62$80.2A$79.A.A$81.A
25$53.2A$54.2A$53.A35$16.3A$18.A$17.A6$8.3A$10.A$9.A6$3A$2.A$.A!

EDIT: A bit simpler:
{109,255, 94,255,256, 95,255,255,111,255,256,145,255,141,256, 91,255, 97,256,116,256, 91,256,256, 90, 0}

x = 1293, y = 1297, rule = LifeHistory
1291.2C$1291.2C4$1289.3A$1291.A$1290.A25$1262.2A$1263.2A$1262.A62$
1198.3A$1200.A$1199.A21$1175.2A$1174.A.A$1176.A62$1111.2A$1112.2A$
1111.A62$1047.2A$1048.2A$1047.A22$1023.3A$1025.A$1024.A61$960.A$960.
2A$959.A.A62$896.2A$895.A.A$897.A26$868.2A$869.2A$868.A62$804.3A$806.
A$805.A62$740.3A$742.A$741.A34$704.2A$705.2A$704.A62$640.3A$642.A$
641.A33$605.2A$606.2A$605.A62$541.2A$542.2A$541.A21$518.3A$520.A$519.
A61$455.A$455.2A$454.A.A23$430.3A$432.A$431.A62$366.3A$368.A$367.A27$
337.3A$339.A$338.A62$273.3A$275.A$274.A20$251.A$251.2A$250.A.A62$187.
A$187.2A$186.A.A62$123.A$123.2A$122.A.A21$100.2A$101.2A$100.A78$20.3A
$22.A$21.A8$10.3A$12.A$11.A8$3A$2.A$.A!
Last edited by simeks on May 26th, 2016, 4:33 pm, edited 1 time in total.
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Re: Orthogonoid working notes

Postby dvgrn » May 26th, 2016, 1:49 pm

simeks wrote:Here's a recipe for a clean eater (integral)...a bit simpler (fishhook eater)...

Nice! Any hope of getting clean *WSS outputs direct from the elbow? They're not needed for the Orthogonoid project, I don't think, but with some oblique geometries it would be possible to build the replicator unit ahead using gliders, and destroy the replicator unit behind using LWSSes, from the same construction arm without any switching streams on and off.

The slow-salvo-to-single-channel compiler is going to be an interesting challenge, I think. Seems likely that there will be a lot of elbow-duplicating (starting from a crystal, maybe, as we've discussed), pulling a spare elbow into position, using it for a while, then jumping back to the original elbow location.
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Re: Orthogonoid working notes

Postby simeks » May 27th, 2016, 5:03 pm

dvgrn wrote:Any hope of getting clean *WSS outputs direct from the elbow?

These two showed up pretty quickly (once I realized that the test for xWSS I tried yesterday only looked for patterns that did not move orthogonally...):
{109,255, 95,255,120,256,255,126,256,149,255,255,107,255,256, 90,256, 91, 0},
{ 93,255,116,255,131,255, 95,255,256,159,255,256,111,256,255,117,256, 90,256, 90,255,102, 0}

x = 1046, y = 1050, rule = LifeHistory
948.2C94.2C$948.2C94.2C4$946.3A93.3A$948.A95.A$947.A95.A21$1019.2A$
1020.2A$1019.A2$919.2A$920.2A$919.A58$955.3A$957.A$956.A2$855.3A$857.
A$856.A21$832.A$832.2A$831.A.A92.3A$928.A$927.A60$768.2A$767.A.A93.A$
769.A93.2A$862.A.A27$738.2A$737.A.A$739.A2$830.2A$829.A.A$831.A58$
674.2A$673.A.A$675.A2$766.2A$767.2A$766.A22$742.3A$744.A$743.A34$610.
2A$611.2A$610.A25$679.A$679.2A$678.A.A2$579.A$579.2A$578.A.A58$615.A$
615.2A$614.A.A2$515.A$515.2A$514.A.A34$575.2A$574.A.A$477.3A96.A$479.
A$478.A60$511.2A$414.A97.2A$414.2A95.A$413.A.A61$447.2A$350.2A96.2A$
349.A.A95.A$351.A25$323.2A94.3A$324.2A95.A$323.A96.A62$259.3A93.3A$
261.A95.A$260.A95.A61$292.A$195.3A94.2A$197.A93.A.A$196.A20$173.2A$
172.A.A$174.A5$262.3A$264.A$263.A55$109.2A$108.A.A$110.A5$198.3A$200.
A$199.A14$86.2A$87.2A$86.A4$176.2A$175.A.A$177.A62$112.2A$111.A.A$
113.A21$89.3A$91.A$90.A61$26.A$26.2A$25.A.A24$2A$.2A$A!

EDIT: Here's even a HWSS:
{109,255, 94,255,255, 95,255,256,175,255,153,255,256,106,256,256,144,256,256, 90,256,255,106,255,116, 0}

x = 1259, y = 1263, rule = LifeHistory
1257.2C$1257.2C4$1255.3A$1257.A$1256.A25$1228.2A$1229.2A$1228.A62$
1164.3A$1166.A$1165.A21$1141.2A$1140.A.A$1142.A62$1077.2A$1078.2A$
1077.A62$1013.3A$1015.A$1014.A21$990.A$990.2A$989.A.A62$926.2A$925.A.
A$927.A62$862.2A$861.A.A$863.A42$818.2A$819.2A$818.A62$754.3A$756.A$
755.A36$716.2A$717.2A$716.A62$652.3A$654.A$653.A62$588.3A$590.A$589.A
24$562.2A$561.A.A$563.A62$498.2A$497.A.A$499.A62$434.2A$433.A.A$435.A
34$398.2A$397.A.A$399.A62$334.2A$333.A.A$335.A62$270.2A$269.A.A$271.A
21$247.3A$249.A$248.A62$183.3A$185.A$184.A61$120.A$120.2A$119.A.A25$
93.2A$94.2A$93.A62$29.3A$31.A$30.A27$3A$2.A$.A!
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Re: Orthogonoid working notes

Postby dvgrn » May 27th, 2016, 6:31 pm

simeks wrote:These two [LWSS recipes] showed up pretty quickly (once I realized that the test for xWSS I tried yesterday only looked for patterns that did not move orthogonally...
EDIT: Here's even a HWSS...

Impressive! So that means a six-direction construction elbow, anyway, and maybe it will be possible to add the last two diagonal directions eventually (0 and 180 degrees).

My one-off optimizer wasn't well written enough that I could really remember how it worked, but I got it to minimize these recipes without too much trouble:

x = 797, y = 504, rule = Life
190b2o98b2o98b2o$190b2o98b2o98b2o$195b3o97b3o97b3o$195bo99bo99bo$196bo
99bo99bo6$2o98b2o$2o98b2o$5b3o97b3o$5bo99bo$6bo99bo11$319b2o$318b2o$
320bo2$223b2o198b2o$222b2o198b2o$224bo199bo8$33b2o98b2o$32b2o98b2o$34b
o99bo99b3o197b3o$234bo199bo$235bo199bo2$338b3o$338bo$339bo4$44b3o97b3o
$44bo99bo$45bo99bo11$258b2o199bo$258bobo197b2o$258bo199bobo3$264bo$
263b2o$263bobo3$68b2o98b2o197b3o$68bobo97bobo196bo$68bo99bo199bo3$74bo
99bo$73b2o98b2o$73bobo97bobo2$377b2o$376b2o$378bo7$285b3o$285bo$286bo
2$489b3o$489bo$490bo3$196bo$95b3o97b2o$95bo99bobo$96bo11$310bo$309b2o
98b3o$309bobo97bo$410bo7$219b2o$219bobo297b3o$219bo299bo$520bo2$323b3o
$323bo101b2o$324bo99b2o$327b2o97bo$327bobo$327bo4$234bo$133b3o97b2o$
133bo99bobo$134bo$138bo98b2o$137b2o97b2o$137bobo98bo2$141b2o$140b2o$
142bo2$145b2o$145bobo$145bo401b2o$547bobo$448b3o96bo$448bo$449bo102bo$
551b2o$551bobo12$264b3o$264bo$265bo4$371b2o$370b2o$372bo$175bo199bo$
174b2o198b2o$174bobo197bobo2$279bo$278b2o$278bobo3$583b2o$582b2o$584bo
3$188b2o97b3o$188bobo96bo$188bo99bo6$496b2o$495b2o$497bo$600bo$599b2o$
599bobo10$211b2o$210b2o$212bo199b3o$412bo$214b3o196bo$214bo$215bo$218b
2o$218bobo$218bo4$324b2o98b2o$323b2o98b2o$325bo99bo$428bo$427b2o$427bo
bo7$536b2o$535b2o99b3o$338b2o197bo98bo$338bobo296bo$338bo6$247bo$246b
2o$246bobo6$454b2o$453b2o$256b2o197bo$255b2o$257bo8$666b2o$665b2o$667b
o3$471b2o$470b2o$374bo97bo$373b2o100bo$373bobo98b2o198b3o$474bobo98b3o
96bo$575bo99bo$576bo2$380b2o$379b2o$381bo2$384b2o$384bobo$384bo4$391bo
$390b2o$390bobo6$298b2o$297b2o$299bo$702bo$701b2o$701bobo2$606bo$605b
2o$605bobo2$309b2o$309bobo199bo$309bo200b2o$510bobo$312b3o$312bo$313bo
100b3o$414bo$415bo$318b2o98b2o$317b2o99bobo99bo$319bo98bo100b2o$519bob
o2$623b2o$622b2o$624bo2$726b3o$726bo$727bo$730b2o$730bobo$730bo$534bo$
533b2o$533bobo8$743b2o$743bobo$743bo2$447b2o297b3o$447bobo296bo$447bo
102bo196bo$549b2o$549bobo98b3o$351b3o296bo$351bo299bo$352bo$454b3o$
454bo$455bo$359bo99bo99bo$358b2o98b2o98b2o$358bobo97bobo97bobo2$562b2o
$362b3o197bobo$362bo199bo$363bo4$770bo$370b2o397b2o$369b2o398bobo$371b
o101bo$472b2o$472bobo2$477bo$476b2o$476bobo2$480b2o298b2o$479b2o298b2o
$381b3o97bo299bo$381bo$382bo5$588b3o$588bo$589bo2$594bo$593b2o$593bobo
2$696b3o$696bo$697bo5$504b2o$504bobo$504bo2$409bo$408b2o$408bobo2$713b
o$712b2o$712bobo8$422b2o199bo$421b2o199b2o$423bo198bobo18$741b3o$643b
2o96bo$643bobo96bo$643bo6$750b3o$750bo$751bo2$756bo$755b2o$755bobo2$
759b2o$758b2o$760bo$763bo$762b2o$762bobo5$769b2o$769bobo$769bo24$794b
3o$794bo$795bo!

Re-run with CIRCUIT_RECOVERY = 90 or whatever, to get glider streams that will work with syringe+Lx200. This version of the script leaves a new layer open in Golly for each optimized recipe, so it will only work for a few recipes at a time without breaking. It will probably need to be rewritten soon anyway, to deal with glider outputs better.

Shortest versions of recipes:
channel-blocking integral:[0, 109, 47, 94, 21, 89, 152, 15, 14, 17, 117, 55, 91, 15, 14, 113, 38, 168, 45, 14, 21, 135, 27, 17, 29, 47, 107, 54]
channel-blocking eater:[0, 109, 47, 94, 21, 88, 95, 57, 14, 111, 55, 37, 145, 57, 141, 26, 17, 25, 97, 14, 116, 30, 15, 56, 16, 14, 97]
135-degree LWSS:[0, 109, 47, 95, 125, 120, 110, 17, 126, 66, 149, 117, 35, 107, 101, 14, 52, 14, 91, 42]
45-degree LWSS:[0, 93, 79, 116, 37, 131, 61, 95, 189, 160, 159, 119, 70, 111, 184, 63, 117, 36, 19, 14, 14, 27, 102, 29]
45-degree HWSS:[0, 109, 47, 94, 21, 89, 95, 57, 14, 175, 14, 153, 45, 14, 106, 68, 14, 144, 36, 56, 64, 36, 15, 106, 19, 116, 83]

Recipes showing adjustment options:
channel-blocking integral:[0,109,47+2N,94,21+2N,89+2N,152,15+2N,14+2N,17+2N,117,55+2N,91,15+2N,14+2N,113,38+2N,168+2N,45+2N,14+2N,21+2N,135,27+2N,17+2N,29+2N,47+2N,107,54+N]
channel-blocking eater:[0,109,47+2N,94,21+2N,88+2N,95,57+2N,14+N,111,55+N,37+N,145,57+2N,141,26+2N,17+2N,25+2N,97,14+2N,116,30+2N,15+2N,56+2N,16+2N,14+2N,97+N]
135-degree LWSS:[0,109,47+2N,95,125+2N,120,110+2N,17+2N,126,66+2N,149,117+2N,35+2N,107,101+2N,14+2N,52+2N,14+2N,91,42+2N]
45-degree LWSS:[0,93,79+2N,116,37+2N,131,61+2N,95,189+2N,160+2N,159,119+2N,70+2N,111,184+2N,63+2N,117,36+N,19+N,14+N,14+N,27+2N,102,29+N]
45-degree HWSS:[0,109,47+2N,94,21+2N,89+2N,95,57+2N,14+N,175,14+N,153,45+2N,14+2N,106,68+2N,14+2N,144,36+2N,56+2N,64+2N,36+2N,15+2N,106,19+N,116,83+N]
Attachments
simeks-revised-27May2016.zip
five recipes minimized with CIRCUIT_RECOVERY=14
(3.48 KiB) Downloaded 163 times
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Re: Orthogonoid working notes

Postby codeholic » May 29th, 2016, 6:52 pm

It seems that you guys still organize fast salvos in pairs, but they don't have to be, do they? I mean, one could use not only pair and singleton gliders, but also triplet, quadruplet etc. Or is it not worth it?
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Re: Orthogonoid working notes

Postby dvgrn » May 29th, 2016, 7:13 pm

codeholic wrote:It seems that you guys still organize fast salvos in pairs, but they don't have to be, do they? I mean, one could use not only pair and singleton gliders, but also triplet, quadruplet etc. Or is it not worth it?

I think it's just that pairs are enough to give plenty of options for universality. Here's the post where simeks decided to go back to searching with pairs of gliders, just for the sake of keeping things simpler for the time being.

I don't know where it starts being impractical to do exhaustive searches involving N-tuples of gliders -- there are a lot of (mostly unlikely) possibilities to sort through, even for triplets.

Every now and then there will be something good out there, though -- it's a huge search space. I'd certainly like to do those searches eventually, but maybe the initial Orthogonoid design can be compiled with a minimal library, and trivially recompiled later if the library improves.

EDIT: Using only pairs of gliders makes it easier to add gaps in the recipe -- which might be useful if we want single-channel streams to cross other streams. That might be really interesting if the timing could be worked out, to make a square Orthogonoid instead of the usual long narrow thing.

With N back-and-forth reflections of the recipe instead of just one, there would be N-1 signal crossings, the upper arm of each higher replicator unit crossing the "forearm" of each lower replicator unit. N new replicator units would be under construction simultaneously. The main thing would be for the beginning of the recipe to get a new target into place by the time 1/N of the recipe is complete, so that the next stream can get started.

-- This probably isn't a good idea at all, but it seems like it may actually be possible, at the cost of cutting down the number of possible periods that the Orthogonoid can be adjusted to.

There's a minimum 90-tick gap between gliders, so I wonder if the output slow-salvo gliders could even be slipped in between without adding any gaps. Given that elbow operations can generate output gliders at very different times, it would probably be necessary to use a seriously restricted set of glider-making elbow ops. That will probably make the recipe several times bigger, so it probably makes more sense just to add gaps instead.

Other than the technical problem of Golly actually simulating all those back-and-forth and crossing streams, it seems as if the design might be made to work. Slow salvo gliders will have to cross a lot of streams, but with three degrees of freedom to work with -- the size of the back-and-forth loop, the distance between loops, and the size of the gaps -- hopefully it will be possible to line up small gaps so they can be re-used.
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Re: Orthogonoid working notes

Postby simeks » June 1st, 2016, 3:44 am

dvgrn wrote:Here's the post where simeks decided to go back to searching with pairs of gliders, just for the sake of keeping things simpler for the time being.

It's perfectly possible to search for salvos of more than two gliders at the current state of the search program, it's just very inefficient. This is one of the things I'm currently trying to improve, and indeed I think there's a lot to be gained to include salvos of more than two gliders, so I really want to implement an efficient way to search for them.

dvgrn wrote:I don't know where it starts being impractical to do exhaustive searches involving N-tuples of gliders -- there are a lot of (mostly unlikely) possibilities to sort through, even for triplets.

I don't think the search space grows all that fast, if only the search program is clever enough to tell the difference between a true salvo, and a collection of gliders that could have been divided in two or more salvos with the same end result.

As a comparison, in the current state of the search program, the number of stable patterns that can be reached from sending a certain number of gliders at an elbow increases by a factor of around 3 for each new glider.

dvgrn wrote:There's a minimum 90-tick gap between gliders, so I wonder if the output slow-salvo gliders could even be slipped in between without adding any gaps. Given that elbow operations can generate output gliders at very different times, it would probably be necessary to use a seriously restricted set of glider-making elbow ops. That will probably make the recipe several times bigger, so it probably makes more sense just to add gaps instead.

My intuition about this, is that it wouldn't have a huge effect on the average recipe size if the timing of emitted gliders needs to be restricted, possibly just a few extra recipe gliders for each emitted glider.
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Re: Orthogonoid working notes

Postby dvgrn » June 1st, 2016, 1:13 pm

simeks wrote:
dvgrn wrote:There's a minimum 90-tick gap between gliders, so I wonder if the output slow-salvo gliders could even be slipped in between without adding any gaps. Given that elbow operations can generate output gliders at very different times, it would probably be necessary to use a seriously restricted set of glider-making elbow ops. That will probably make the recipe several times bigger, so it probably makes more sense just to add gaps instead.

My intuition about this, is that it wouldn't have a huge effect on the average recipe size if the timing of emitted gliders needs to be restricted, possibly just a few extra recipe gliders for each emitted glider.

Yeah, that makes sense -- especially in the case where recipes are made mostly out of pairs of gliders. There will be a certain amount of adjustability in a lot of recipes, to move Glider Pair #2 relative to Glider Pairs #1 and #3 for example, in whatever way is needed to keep the output glider in the safe zone.

This square-Orthogonoid design seems strangely interesting, with stacks of maybe dozens or hundreds of 180-degree MWSS reflector/construction arms on each side, and the leading half of them increasingly incomplete as you go up. But I'm not sure it's going to turn out to be practical. It may end up with by far the smallest long-axis measurement of any engineered macro-spaceship, and by far the lowest period... but it may also have so many back-and-forth data streams in close proximity that Golly will get bogged down completely trying to run the pattern.

... That's assuming that the timing can be worked out so that there's always a gap in every single-channel stream heading for the elbow, when each output slow-salvo glider crosses that stream. It's not a foregone conclusion, but I think there's enough adjustability in the system that it might turn out to be possible. Will build a sample and find out, when I get a chance --
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Re: Orthogonoid working notes

Postby simeks » June 3rd, 2016, 6:16 pm

dvgrn wrote:The slow-salvo-to-single-channel compiler is going to be an interesting challenge, I think. Seems likely that there will be a lot of elbow-duplicating (starting from a crystal, maybe, as we've discussed), pulling a spare elbow into position, using it for a while, then jumping back to the original elbow location.

Here's a simpler way to do this:

x = 1906, y = 1909, rule = LifeHistory
1904.2A$1904.2A7$1899.2A$1898.A.A$1900.A25$1872.A$1872.2A$1871.A.A78$
1792.2A$1791.A.A$1793.A22$1768.3A$1770.A$1769.A78$1688.2A$1689.2A$
1688.A78$1608.3A$1610.A$1609.A40$1566.2A$1565.A.A$1567.A78$1486.2A$
1485.A.A$1487.A78$1406.2A$1405.A.A$1407.A78$1326.A$1326.2A$1325.A.A
78$1246.2A$1245.A.A$1247.A78$1166.2A$1165.A.A$1167.A26$1138.3A$1140.A
$1139.A253$883.3A$882.3BA$882.2BA$883.B29$851.3A$850.3BA$850.2BA$851.
B203$645.2A$644.A.A$646.A25$618.A$618.2A$617.A.A78$538.2A$537.A.A$
539.A23$513.2A$514.2A$513.A78$433.3A$435.A$434.A78$353.3A$355.A$354.A
78$273.2A$274.2A$273.A26$245.A$245.2A$244.A.A209$34.3A$36.A$35.A31$.A
$.2A$A.A!

EDIT: Related to this, there's no shortage of LWSS and MWSS recipes even if you want to have the elbow back. One HWSS in this search too, but they are a bit rarer:

x = 2967, y = 3797, rule = LifeHistory
1365.2A$1365.2A7$1360.2A$1359.A.A$1361.A25$1333.A$1333.2A$1332.A.A27$
1429.2A$1429.2A7$1424.2A$1423.A.A$1425.A21$1401.A$1401.2A$1400.A.A13$
1358.2A$1358.2A4$1253.A$1253.2A$1252.A.A11$1493.2A$1493.2A7$1488.2A$
1487.A.A$1489.A$1229.3A$1231.A$1230.A22$1461.A$1461.2A$1460.A.A10$
1321.2A$1320.A.A$1322.A15$1557.2A$1557.2A7$1552.2A$1551.A.A$1553.A2$
1292.2A$1291.A.A$1293.A6$1451.2A$1451.2A6$1149.2A$1150.2A$1149.A10$
1521.2A$1520.A.A$1522.A10$1381.2A$1380.A.A$1382.A11$1621.2A$1621.2A7$
1616.2A$1615.A.A$1617.A$1357.3A$1359.A$1358.A15$1212.A$1212.2A$1211.A
.A5$1589.A$1589.2A$1588.A.A6$1069.3A$1071.A$1070.A10$1441.2A$1440.A.A
$1442.A4$1179.2A$1178.A.A$1180.A$1685.2A$1685.2A7$1680.2A$1679.A.A$
1681.A7$1031.2A$1032.2A$1031.A8$1277.2A$1278.2A$1277.A6$1653.A$1653.
2A$1652.A.A14$1509.2A$1508.A.A$1510.A11$1749.2A$1749.2A6$1361.A$1361.
2A381.2A$1360.A.A380.A.A$1745.A$1485.3A$1487.A$1099.A386.A$1099.2A$
1098.A.A18$951.3A$953.A$952.A764.A$1717.2A$1075.2A639.A.A$1074.A.A$
1076.A4$1197.3A$1199.A$1198.A6$1573.A$1573.2A$1572.A.A11$1813.2A$
1813.2A7$1808.2A$1807.A.A$1166.3A640.A$1168.A380.3A$1167.A383.A$1550.
A10$1281.A$1281.2A$1280.A.A2$1405.2A$1406.2A$1405.A6$1781.A$1781.2A$
1780.A.A12$871.3A$873.A$872.A764.2A$1636.A.A$995.A642.A$995.2A$994.A.
A9$1877.2A$1877.2A7$1872.2A$1871.A.A$1614.A258.A$1614.2A$1613.A.A14$
1086.3A$1088.A380.2A$1087.A382.2A$1469.A6$1845.A$1845.2A$1844.A.A2$
1201.2A$1200.A.A$1202.A2$1325.3A$1327.A$1326.A5$1062.2A$1061.A.A637.
2A$1063.A636.A.A$1702.A11$1941.2A$791.2A1148.2A$792.2A$791.A2$915.A$
915.2A$914.A.A$1936.2A$1935.A.A$1937.A$1293.3A381.3A$1295.A383.A$
1294.A383.A13$766.2A766.2A$767.2A764.A.A$766.A768.A3$1913.A$1913.2A$
1912.A.A10$1389.2A$1390.2A$875.2A512.A$874.A.A$876.A4$1765.2A$1764.A.
A$1766.A2$1121.2A$1120.A.A$1122.A$1502.A$1502.2A$1501.A.A4$2005.2A$
2005.2A$982.A$982.2A381.3A$981.A.A383.A$1366.A3$2000.2A$1999.A.A$
1742.A258.A$1742.2A$1741.A.A2$1899.2A$1899.2A12$1213.3A381.2A$1215.A
382.2A$1214.A382.A6$1973.A$1973.2A$1972.A.A5$686.2A$687.2A$686.A$939.
2A$938.A.A$940.A892.2A$1832.A.A$1834.A12$795.A$795.2A$794.A.A$2069.2A
$2069.2A3$660.2A$661.2A$660.A$1041.2A766.A$1040.A.A766.2A253.2A$1042.
A765.A.A252.A.A$1422.2A641.A$1421.A.A$1423.A7$1285.2A$1286.2A$1285.A
5$1662.2A$1661.A.A$1663.A7$2037.A$2037.2A$2036.A.A6$1133.3A381.3A$
1135.A383.A$1134.A383.A6$1893.2A$1892.A.A$1894.A7$1628.A$859.A768.2A$
859.2A766.A.A$858.A.A$2133.2A$2133.2A7$2128.2A$2127.A.A$1870.A258.A$
1870.2A$1869.A.A$715.A767.3A$715.2A768.A$714.A.A767.A4$1093.2A$580.3A
511.2A$582.A510.A$581.A$961.2A766.2A$960.A.A765.A.A$962.A767.A$1342.A
$1342.2A$1341.A.A7$1205.3A893.A$1207.A893.2A$1206.A893.A.A2$817.A$
817.2A$687.2A127.A.A$686.A.A$688.A8$1957.2A$1956.A.A$1958.A7$924.2A$
923.A.A$925.A2$2197.2A$1175.A1021.2A$1175.2A$1174.A.A5$2192.2A$2191.A
.A$1934.A258.A$1934.2A$1548.A384.A.A$1548.2A$1547.A.A12$1790.A$1790.
2A$1789.A.A$1403.2A$1404.2A$1403.A4$1013.3A$500.3A512.A$502.A511.A$
501.A$1649.A511.2A$1649.2A509.A.A$1648.A.A511.A$1262.A$1262.2A$1261.A
.A6$1510.2A$1509.A.A509.2A$1511.A508.A.A$2022.A2$737.2A$736.A.A$607.
2A129.A$606.A.A$477.2A129.A1148.2A$478.2A1278.2A$477.A1279.A3$2261.2A
$1623.2A636.2A$1622.A.A$1624.A5$2256.2A$2255.A.A$2257.A$1997.2A$844.A
1153.2A$844.2A1151.A$843.A.A$713.2A$712.A.A$714.A380.A$1095.2A$1094.A
.A7$1854.2A$1853.A.A$1855.A7$2229.A$2229.2A$2228.A.A8$1323.3A$1325.A$
1324.A4$933.3A$935.A$934.A$2186.2A$2081.2A103.2A$2080.A.A$2082.A$
1182.A$1182.2A$1181.A.A$1819.2A$1818.A.A$1820.A$2325.2A$2325.2A$1430.
A$1430.2A$1429.A.A4$2320.2A$527.A1791.A.A$527.2A1792.A$397.3A126.A.A
1148.3A$399.A1279.A$398.A1279.A$906.2A$907.2A$906.A$1543.A$1543.2A$
1542.A.A4$1153.3A$1155.A$1154.A2$1917.3A$764.2A1153.A$763.A.A1152.A$
765.A$633.A$633.2A$632.A.A380.2A$1014.A.A$1016.A380.2A894.A$1398.2A
893.2A$1397.A894.A.A2$497.3A$499.A$498.A10$2149.2A$2148.A.A$2150.A$
1506.2A$1507.2A380.3A$1506.A384.A$1890.A3$2343.2A$987.3A253.3A1097.2A
$989.A255.A$988.A255.A$2389.2A$2389.2A6$2001.A$2001.2A381.2A$591.3A
1406.A.A380.A.A$593.A1791.A$592.A1532.3A$2127.A$1739.A386.A$1739.2A$
1738.A.A12$317.3A1277.2A$319.A892.2A384.2A$318.A892.A.A383.A$826.3A
384.A$828.A$827.A3$2357.A$2357.2A$2356.A.A$1714.3A$1073.3A640.A$1075.
A639.A$1074.A3$684.A$684.2A$683.A.A5$1317.2A894.2A$1318.2A892.A.A$
1317.A896.A2$417.3A$419.A$418.A7$2453.2A$2453.2A2$1557.2A$1556.A.A$
1558.A$1426.2A$1427.2A380.3A$1426.A384.A636.2A$1810.A636.A.A$2190.A
258.A$2190.2A$2189.A.A$907.3A$909.A$908.A5$1284.2A$1285.2A$1284.A$
1921.A$1921.2A$511.3A1406.A.A$513.A$512.A1532.2A$2046.2A$2045.A2$
1401.3A$1403.A$1402.A2$2421.A$2421.2A$2420.A.A6$237.3A1533.2A$239.A
892.2A640.2A$238.A892.A.A639.A$746.3A384.A$748.A$747.A3$485.A1791.2A$
485.2A1789.A.A$484.A.A380.A1410.A$867.2A765.2A$866.A.A124.2A640.2A$
994.2A638.A$993.A3$604.2A$603.A.A$605.A2$2517.2A$2517.2A3$1108.A$
1108.2A$1107.A.A$337.3A$339.A2172.2A$338.A2172.A.A$2254.A258.A$2254.
2A$2253.A.A2$970.A$970.2A$969.A.A3$1477.A$1477.2A$1476.A.A5$2110.2A$
2109.A.A$2111.A3$1593.A$1593.2A$1592.A.A2$2485.A$1204.2A1279.2A$1205.
2A1277.A.A$1204.A$1841.2A$1840.A.A$1842.A2$1965.3A$1967.A$1966.A2$
1321.3A$1323.A$1322.A2$2341.2A$2340.A.A$1443.2A897.A$1442.A.A$1444.A
2$2079.2A$2080.2A$157.3A1533.3A383.A$159.A1535.A$158.A1535.A$666.3A$
668.A$667.A508.2A1403.2A$1175.A.A1403.2A$1177.A764.3A$405.A1538.A$
405.2A1536.A$404.A.A380.A$787.2A$786.A.A$2576.2A$2575.A.A$2577.A$
1293.A1023.3A$524.2A767.2A1024.A$523.A.A766.A.A1023.A$525.A6$1028.A$
1028.2A$130.2A895.A.A$129.A.A125.3A$131.A127.A$258.A380.2A$638.A.A
1533.2A$640.A1532.A.A$2175.A271.2A$2447.2A$890.2A$889.A.A$891.A3$
2549.A$2549.2A$371.2A126.A2048.A.A$370.A.A126.2A$372.A125.A.A4$1005.
2A$1006.2A$1005.A2$1513.2A$1512.A.A$1514.A2$2405.2A$2404.A.A$2406.A2$
1761.2A$1760.A.A$1762.A3$2140.A$859.A1280.2A$859.2A1278.A.A$858.A.A$
2645.2A$2645.2A4$1363.2A$1362.A.A$1364.A$2640.2A$1999.2A638.A.A$2000.
2A639.A$1613.3A383.A381.3A$1615.A767.A$1614.A767.A3$1096.2A$1095.A.A$
1097.A764.3A$1864.A$1863.A$707.2A$706.A.A$708.A4$1213.2A1022.2A$1212.
A.A1023.2A$1214.A1022.A6$2613.A$2613.2A$2612.A.A2$177.3A1789.3A$179.A
1791.A$178.A380.2A1409.A$558.A.A$560.A$1068.3A$1070.A$682.A386.A764.
2A$682.2A1151.2A$681.A.A1150.A2$1574.2A$1575.2A892.2A$1574.A893.A.A$
291.2A126.A2050.A$290.A.A126.2A$292.A125.A.A4$925.2A$926.2A$925.A2$
1433.A$1433.2A1274.2A$1432.A.A1274.2A4$531.2A$532.2A$531.A1149.2A$
1680.A.A1021.2A$1682.A1020.A.A$2705.A$2445.3A$2060.A386.A$779.2A1279.
2A384.A$394.2A382.A.A1278.A.A$395.2A383.A$394.A5$899.A383.2A$899.2A
381.A.A$898.A.A383.A4$2301.2A$2302.2A$2301.A4$1399.2A$1398.A.A$1400.A
1276.A$2677.2A$2676.A.A4$751.2A$752.2A$751.A381.2A1022.3A$1132.A.A
1024.A$1134.A1023.A3$2024.A$2024.2A$2023.A.A$2533.2A$2532.A.A$2534.A
2$97.2A1790.2A$98.2A1790.2A$97.A1791.A3$988.3A$990.A$602.A386.A764.3A
$602.2A1152.A$601.A.A1151.A1017.2A$2773.2A$1494.3A$1109.2A385.A$1108.
A.A384.A$211.A898.A$211.2A$210.A.A$2768.2A$2767.A.A$2510.A258.A$2510.
2A$2509.A.A$2123.3A$2125.A$2124.A5$964.3A$451.3A512.A$453.A511.A$452.
A1148.2A$1600.A.A$1602.A2$61.A2303.2A$61.2A125.A2177.2A$60.A.A125.2A
2175.A$187.A.A124.3A$316.A$315.A3$565.2A2174.A$564.A.A2174.2A$566.A
252.2A382.2A1535.A.A$818.A.A381.A.A$820.A383.A4$2221.3A$2223.A$2222.A
4$1319.A$1319.2A$1318.A.A1276.2A$420.3A2173.A.A$422.A2175.A$421.A3$
671.3A2023.2A$673.A2023.2A$672.A2$795.3A$797.A$796.A$1560.3A381.2A
891.2A$1562.A380.A.A891.2A$1561.A383.A5$1809.2A$1810.2A1020.2A$1809.A
1021.A.A$2833.A$1293.2A894.3A381.3A$1292.A.A896.A383.A$1294.A895.A
383.A$1674.2A$1675.2A$1674.A2$1414.2A$1029.2A384.2A$1028.A.A383.A$
643.A386.A$643.2A$642.A.A3$2430.A$2430.2A$2429.A.A$2043.3A$2045.A$
1913.A130.A$1913.2A$1783.3A126.A.A$1785.A$1784.A1020.A$884.3A765.A
1152.2A$886.A765.2A1150.A.A$885.A765.A.A5$2285.2A$2286.2A$2285.A$234.
3A$236.A$235.A3$485.2A2174.2A$484.A.A2173.A.A$486.A636.2A1537.A$1122.
A.A$1124.A8$857.2A$856.A.A2042.2A$858.A2042.2A3$340.3A$342.A2044.2A$
341.A2044.A.A$2388.A$2896.2A$2895.A.A$2638.A258.A$2638.2A$2637.A.A$
715.3A$717.A$716.A$1480.2A$1095.2A384.2A764.2A$1096.2A382.A767.2A$
1095.A1151.A8$1213.A895.3A381.2A$1213.2A896.A382.2A$1212.A.A895.A382.
A5$1334.2A$949.2A384.2A1532.A$948.A.A383.A1534.2A$563.2A385.A1917.A.A
$562.A.A2282.2A$564.A2282.2A6$1963.3A$1965.A$1449.2A382.2A129.A$1450.
2A380.A.A$1449.A253.3A128.A$1705.A$1704.A1020.2A$1572.A1151.A.A$1572.
2A1152.A$1571.A.A7$1179.3A$154.3A1024.A124.2A$156.A1023.A124.A.A$155.
A1151.A1657.2A$2965.2A2$405.2A$404.A.A$406.A3$2960.2A$2959.A.A$2961.A
$2701.3A$2703.A$2702.A2$777.A$777.2A$776.A.A3$260.3A$262.A2044.2A$
261.A2044.A.A$2308.A$2841.2A$2841.2A$2558.A$2558.2A$2557.A.A$635.2A$
636.2A$635.A$376.3A$378.A636.2A1150.3A$377.A638.2A1151.A$1015.A1152.A
764.A$2933.2A$2932.A.A3$112.2A$113.2A$112.A$2029.3A381.2A$2031.A382.
2A$2030.A382.A6$869.A1919.2A$869.2A1917.A.A$483.A384.A.A1919.A$483.2A
$482.A.A3$606.2A$605.A.A$607.A$987.2A894.3A$986.A.A896.A$988.A380.3A
381.2A129.A$1371.A380.A.A$1370.A252.3A128.A$1625.A$1624.A$1492.A$
1492.2A1021.3A$1491.A.A1023.A$2516.A4$2765.3A$1996.2A769.A$1099.3A
895.2A767.A$1101.A124.2A768.A$1100.A124.A.A$840.2A385.A$841.2A1532.2A
$840.A1535.2A$2375.A5$1600.2A$1599.A.A$1601.A$2621.2A$1852.3A767.2A$
1854.A766.A$1853.A$697.A$697.2A637.3A$696.A.A639.A$1337.A2$180.2A$
181.2A1276.2A766.2A$180.A1021.2A254.A.A765.A.A$1201.A.A256.A767.A$
1203.A8$296.2A$297.2A764.3A1021.3A$296.A768.A1023.A$1064.A1023.A764.
2A$2852.A.A$2854.A3$32.2A$33.2A$32.A11$403.2A$402.A.A$404.A3$526.2A$
525.A.A2301.3A$527.A2303.A$907.A1922.A$907.2A$906.A.A764.2A$1672.A.A$
1674.A4$2435.3A$2437.A$2436.A$2A$.2A$A$2685.2A$1916.3A767.2A$1918.A
766.A$1917.A2$760.3A$762.A1532.3A$761.A1535.A$2296.A$884.A$884.2A$
883.A.A2$1520.A$1520.2A$1519.A.A$2541.3A$1772.3A768.A$1774.A767.A$
1773.A$617.A$617.2A637.3A$616.A.A639.A$1257.A2$100.3A$102.A1276.2A
766.2A$101.A1020.2A254.A.A765.A.A$1121.A.A256.A767.A$1123.A5$1883.3A$
1885.A$1884.A$216.2A$217.2A764.3A1021.2A$216.A768.A1022.2A508.A$984.A
1022.A510.2A$2517.A.A10$1098.A$1098.2A$1097.A.A380.3A$1482.A$1481.A3$
323.2A$322.A.A$193.2A129.A$64.3A127.2A$66.A126.A$65.A380.A$446.2A
2301.2A$445.A.A2302.2A$2749.A2$1593.A$1593.2A$1592.A.A4$947.2A1022.2A
382.2A$948.2A1020.A.A383.2A$947.A1024.A382.A4$2605.3A$2607.A$2606.A3$
680.3A$423.2A257.A1532.3A$424.2A255.A1535.A$423.A1792.A$804.A$804.2A$
290.A512.A.A$290.2A$289.A.A4$1692.3A$1694.A$1693.A$537.2A$536.A.A637.
2A$538.A638.2A$1176.A2$2324.3A$1299.2A766.A258.A$1298.A.A766.2A256.A$
1300.A765.A.A4$781.2A$782.2A$781.A1021.2A766.3A$1804.2A767.A$1803.A
768.A3$2438.2A$2437.A.A$2439.A3$1665.2A$1666.2A$1665.A3$1148.2A$1149.
2A$506.A511.A129.A$506.2A510.2A$505.A.A509.A.A380.3A$1402.A$1401.A$
2037.2A$2038.2A$2037.A4$1775.2A$1774.A.A$1776.A892.3A$2671.A$2670.A2$
1513.A$1513.2A$1512.A.A4$867.2A1022.2A$868.2A1020.A.A$867.A1024.A3$
990.2A$989.A.A$991.A4$600.3A$343.3A256.A1532.2A$345.A255.A1534.2A$
344.A1790.A3$210.2A$209.A.A$211.A$1359.A$1359.2A$1358.A.A2$2635.3A$
2637.A$2636.A5$2244.2A$1219.2A1024.2A$1218.A.A1023.A$1220.A$320.2A$
321.2A$320.A$701.2A126.2A$702.2A124.A.A$701.A128.A1660.3A$2106.2A385.
A$2105.A.A384.A$2107.A2$2358.2A$2357.A.A$2359.A$179.2A$178.A.A$180.A
1404.2A$560.2A1024.2A$559.A.A1023.A$561.A2$1068.3A$1070.A$426.A642.A$
426.2A$425.A.A3$1957.3A$1959.A$1958.A4$1695.A$1695.2A$1694.A.A4$1433.
2A$1432.A.A$1434.A$1558.2A$1559.2A$1558.A765.A$1811.2A511.2A$1810.A.A
510.A.A$1812.A2$399.2A$400.2A508.2A$399.A509.A.A$911.A$1035.2A$1034.A
.A$1036.A10$1279.2A$1278.A.A$1280.A2$2555.2A$2556.2A$2555.A2$1783.A$
1783.2A$1782.A.A$2164.3A$1139.2A1025.A$1138.A.A1024.A$881.2A257.A$
882.2A$881.A2$621.3A125.A$623.A125.2A$622.A125.A.A1660.3A$2026.2A385.
A$2025.A.A384.A$2027.A8$480.A$480.2A$479.A.A6$2136.2A$2135.A.A$2137.A
$1877.2A$1878.2A$1877.A4$1615.A$1615.2A$717.3A894.A.A$719.A$718.A2$
585.A767.2A$585.2A765.A.A$584.A.A767.A$1478.2A$1479.2A$1478.A765.A$
2244.2A$2243.A.A3$319.3A$321.A$320.A2$955.A895.2A$955.2A895.2A$954.A.
A894.A10$1199.A127.3A$1199.2A128.A$1198.A.A127.A252.3A$1583.A$1582.A
892.3A$2477.A$2476.A2$1703.2A$1702.A.A$1704.A2$1059.2A$1058.A.A$801.
2A257.A$802.2A$801.A4$2331.3A$1946.2A385.A$1945.A.A384.A$1947.A8$400.
A$400.2A$399.A.A6$2056.2A$2055.A.A$2057.A2$2308.A$2308.2A$2307.A.A5$
637.3A$639.A$638.A2$505.2A$504.A.A$506.A$1398.2A$1399.2A$1398.A765.2A
$2163.A.A$2165.A7$875.2A894.3A$874.A.A896.A$876.A895.A10$1119.2A126.
3A$1118.A.A128.A$1120.A127.A252.2A$1502.2A$1501.A893.3A$2138.A258.A$
2138.2A256.A$2137.A.A$1623.2A$1622.A.A$1624.A2$979.A$979.2A$721.3A
254.A.A$723.A$722.A5$1866.2A$1865.A.A$1867.A4$1732.2A$1733.2A$1732.A
2$320.A$320.2A$319.A.A$2365.3A$2367.A$2366.A3$1976.A$1463.3A510.2A$
1465.A509.A.A$1464.A$2228.A$2228.2A$2227.A.A5$557.3A$559.A$558.A2$
297.A127.A$297.2A126.2A$296.A.A125.A.A$1318.3A$1320.A$1319.A5$1951.A$
1951.2A$1950.A.A2$795.2A$794.A.A$796.A1404.2A$2202.2A$2201.A8$1039.2A
126.2A$1038.A.A127.2A$1040.A126.A3$2058.2A$1289.2A766.A.A$1290.2A767.
A$1289.A253.A$1543.2A$1542.A.A2$899.A$899.2A$641.3A254.A.A$643.A$642.
A5$1786.2A$1785.A.A$1787.A4$1652.3A$1654.A$1653.A5$2285.3A$2287.A$
1515.2A769.A$1516.2A$1515.A2$1383.3A637.3A$1385.A639.A$1384.A639.A$
1124.2A$1125.2A$1124.A5$477.2A$478.2A$477.A2$217.2A126.A$216.A.A126.
2A$218.A125.A.A8$1871.2A$1358.3A509.A.A$1360.A511.A$1359.A$715.A$715.
2A$714.A.A1404.2A$2122.2A$2121.A$2246.2A$2245.A.A$2247.A5$959.A$959.
2A$958.A.A$316.3A$318.A$317.A124.3A$444.A764.3A$443.A767.A636.3A$
1210.A639.A$1849.A3$819.A$819.2A$561.3A254.A.A$563.A$562.A5$1706.2A$
1705.A.A$1707.A4$1572.3A$931.2A641.A$932.2A639.A$931.A6$1435.3A$794.A
642.A$794.2A640.A$793.A.A$1943.3A$1945.A$1944.A$1044.2A$1045.2A$1044.
A20$1278.2A$1279.2A$1278.A$635.A$635.2A$634.A.A1404.2A$2042.2A$2041.A
$2166.2A$1397.A767.A.A$1397.2A768.A$1396.A.A10$1129.2A$1130.2A636.2A$
1129.A639.2A$1768.A2$612.2A$613.2A$612.A$481.3A$483.A$482.A5$1626.2A$
1625.A.A$1627.A4$1492.3A$851.3A640.A$853.A639.A508.A$852.A892.2A255.
2A$1746.2A253.A.A$1745.A5$714.2A$457.A255.A.A$457.2A256.A$456.A.A
1404.3A$1865.A$1864.A$964.3A$966.A$965.A14$1460.A$1460.2A$1459.A.A3$
1839.2A$1198.3A639.2A$1200.A638.A$1199.A4$936.2A$937.2A$936.A1149.A$
1317.2A767.2A$1316.A.A766.A.A$1318.A10$1049.2A$1050.2A$1049.A3$532.3A
$534.A$533.A5$1165.3A$1167.A124.3A$1166.A127.A764.3A$1293.A252.2A513.
A$1545.A.A512.A$1547.A5$771.3A$773.A1148.2A$772.A892.2A254.A.A$1666.
2A255.A$1665.A5$634.2A$377.A255.A.A$377.2A256.A$376.A.A12$491.3A$493.
A$492.A5$1380.2A$1379.A.A$1381.A3$1759.2A$1760.2A$1759.A5$856.3A$858.
A$857.A13$969.3A$971.A$970.A7$832.3A$834.A$833.A$1085.2A$1086.2A124.
3A$1085.A128.A764.2A$1213.A252.2A512.2A$1465.A.A511.A$1467.A5$691.3A$
693.A1148.2A$692.A892.3A253.A.A$1587.A255.A$1586.A5$554.2A$297.A255.A
.A$297.2A256.A$296.A.A6$1185.A$1185.2A253.2A$1184.A.A254.2A$1440.A3$
411.3A$413.A$412.A4$1813.3A$1300.A514.A$1300.2A512.A$1299.A.A3$1679.
3A$1681.A$1680.A20$889.3A$891.A$890.A7$752.2A$753.2A$752.A$1005.3A$
1007.A$1006.A892.2A$1900.2A$1899.A6$611.3A$613.A$612.A892.3A$1507.A$
1506.A5$474.2A$473.A.A$475.A7$1105.A$1105.2A253.2A$1104.A.A254.2A$
1360.A3$331.2A$332.2A$331.A4$1733.3A$1220.2A513.A$1219.A.A512.A124.3A
$1221.A639.A$1860.A2$1599.2A$1600.2A$1599.A5$568.2A$569.2A$568.A13$
809.3A$811.A$810.A$294.A$294.2A$293.A.A4$672.3A$674.A$673.A$925.2A$
926.2A$925.A10$1425.2A$1426.2A$1425.A5$394.2A$393.A.A$395.A4$772.2A$
773.2A$772.A$1025.2A$1024.A.A253.3A$1026.A255.A$1281.A9$1653.3A$884.A
255.A255.3A256.A$884.2A254.2A256.A255.A124.3A$883.A.A253.A.A255.A383.
A$369.2A1409.A$370.2A$369.A1149.3A$1521.A$1520.A5$488.2A$489.2A$488.A
10$1116.2A$1115.A.A$1117.A636.2A$1753.A.A$1755.A2$214.2A$213.A.A$215.
A4$592.3A1021.2A$594.A1022.2A$593.A1022.A26$692.2A$693.2A$562.3A127.A
$564.A380.2A$563.A380.A.A253.3A$946.A255.A$1201.A10$804.A511.3A$804.
2A512.A$803.A.A511.A$289.2A$290.2A$289.A1149.2A$1440.2A$1439.A5$408.
2A$409.2A$408.A10$1036.2A$1035.A.A$1037.A636.2A$1673.A.A$1675.A$903.
3A$905.A$904.A5$1536.2A$1537.2A$1536.A12$1650.2A$1649.A.A$1651.A12$
612.2A$613.2A$482.2A128.A$483.2A508.2A$482.A509.A.A125.3A$994.A127.A$
1121.A10$724.A511.3A$724.2A512.A$723.A.A511.A$209.2A$210.2A$209.A
1149.2A$1360.2A$1359.A5$328.3A765.A$330.A765.2A$329.A765.A.A12$698.A$
698.2A$697.A.A$823.3A$825.A$824.A4$1329.2A$1328.A.A125.2A$1330.A126.
2A$1456.A12$1570.2A$1569.A.A$1571.A12$532.2A$533.2A$402.3A127.A$404.A
508.2A$403.A508.A.A$914.A11$1156.3A$1158.A$1157.A10$248.3A765.2A$250.
A764.A.A$249.A252.2A513.A$503.2A$502.A9$1131.3A$618.2A513.A$617.A.A
512.A$619.A$743.3A$745.A$744.A4$1249.2A$1248.A.A125.3A$1250.A127.A$
1377.A2$988.2A$987.A.A$989.A8$1490.2A$1489.A.A$1491.A3$717.3A$719.A$
718.A7$1348.3A$1350.A$322.3A1024.A$324.A508.2A$323.A508.A.A$834.A23$
168.3A$170.A$169.A252.3A$424.A$423.A9$1051.3A$538.A514.A$538.2A512.A$
537.A.A7$1169.2A$1168.A.A$1170.A3$908.2A$907.A.A$909.A7$1027.3A$1029.
A380.2A$1028.A380.A.A$1411.A3$637.3A$639.A$638.A7$1268.3A$1270.A$242.
2A1025.A$243.2A508.A$242.A510.2A$752.A.A22$1241.A$1241.2A$1240.A.A$
342.3A$344.A$343.A10$458.2A$457.A.A$459.A7$1089.A$1089.2A$1088.A.A3$
828.A$828.2A$827.A.A7$947.2A$948.2A380.A$947.A382.2A$1329.A.A3$557.3A
$559.A$558.A10$673.A127.2A$673.2A127.2A$672.A.A126.A8$1047.2A$1048.2A
$1047.A11$650.2A$649.A.A509.2A$651.A508.A.A$1162.A$262.2A$263.2A$262.
A33$867.2A$868.2A380.A$867.A382.2A$1249.A.A3$477.2A$478.2A$477.A10$
721.2A$722.2A$721.A8$967.2A$968.2A$967.A6$1215.3A$1217.A$1216.A3$570.
A$570.2A509.A$569.A.A509.2A$1080.A.A36$787.2A$788.2A$787.A16$641.3A$
643.A$642.A8$887.2A$888.2A$887.A6$1135.2A$1136.2A$1135.A$748.2A$747.A
.A$490.2A257.A$489.A.A509.2A$491.A508.A.A$1002.A10$861.2A$862.2A$861.
A3$1112.A$1112.2A$1111.A.A37$561.2A$562.2A$561.A22$921.A$921.2A$920.A
.A$534.2A$533.A.A$535.A7$781.3A$783.A$782.A3$1032.A$1032.2A$1031.A.A
39$991.2A$992.2A$991.A20$841.2A$840.A.A$842.A10$701.2A$702.2A$701.A
44$911.3A$913.A$912.A20$761.2A$760.A.A$762.A10$621.3A$623.A$622.A21$
726.A$726.2A$725.A.A21$831.3A$833.A$832.A21$808.2A$809.2A$808.A32$
646.2A$645.A.A$647.A!
simeks
 
Posts: 344
Joined: March 11th, 2015, 12:03 pm
Location: Sweden

Re: Orthogonoid working notes

Postby dvgrn » June 7th, 2016, 1:10 pm

simeks wrote:EDIT: Related to this, there's no shortage of LWSS and MWSS recipes even if you want to have the elbow back. One HWSS in this search too, but they are a bit rarer...

Impressive -- I didn't expect to see elbow-preserving single-channel *WSS recipes that were quite this cheap. The first couple of LWSS outputs are 21 and 23 gliders.

Could probably use these to reduce the height of an Orthogonoid a little bit, by shooting LWSSes at the previous opposite replicator unit, to clean it up. But the total population would go way up, and I don't see any other advantages to doing the cleanup that way -- gliders knocking out the "next door" replicator unit are much easier.

I guess cleanup with *WSSes will have to wait until someone puts together an oblique single-channel Geminoid, as the linked post mentioned. For some designs that would be really elegant.

Do you have lists of glider spacings handy, or should I just extract them from the RLE?

EDIT: On a different line of research, there appear to be plenty of ways to get a glider to the H-to-MWSS circuit to suppress the beehive. The original Stage 0 pure-stable design has four eater2s and a population of 371, not counting the switching circuitry which might change. Here are a couple of alternatives with seventy-odd more ON cells, but only two eater2s:

Orthogonoid446:
x = 119, y = 216, rule = LifeHistory
98.2A$98.2A11$69.A42.2A$69.3A40.A.A$72.A41.A$71.2A41.2A5$102.3D$74.2D
17.2A8.D$73.D2.D17.A6.3D$74.2D9.A5.3A$58.D25.A.A4.A$56.D3.D24.2A$55.D
$55.D4.D$55.5D49.2E$109.E.E$111.E$111.2E7$101.2A$92.2A7.2A$74.2A17.A$
74.2A17.A.A7.D$94.2A6.3D$73.3D25.2D2.D$74.D$72.3D37.2A$112.A$110.A.A$
110.2A3$96.2A$95.A.A$95.A$94.2A6$108.3D$72.2A25.2A8.D$63.2A7.2A26.A6.
3D$64.A32.3A$23.A40.A.A7.D22.A$23.3A33.2A4.2A6.3D$10.2A3.2A9.A17.A15.
A11.2D2.D4.2A$10.2A3.2A8.2A15.3A15.A.A18.A$41.A19.2A16.A.A33.2A$41.2A
36.2A34.A.A$3.2A112.A$4.A112.2A$4.A.A$5.2A2$40.D3.2A15.D$40.2D2.2A15.
D.D$41.2D18.3D$41.D21.D43.2A$40.D66.2A$8.2A63.2A$9.A63.2A2.2A22.A7.D$
6.3A28.2A38.A.A19.3A6.3D$6.A31.A15.2A23.A18.A8.2D2.D$35.3A17.A23.2A
17.2A$35.A16.3A$52.A64.2A$116.A.A$116.A$115.2A$21.2A$21.2A$13.2A$14.A
6.3D72.2A$11.3A8.D74.A$11.A10.3D72.A.A$98.2A15.2A$12.A102.2A$11.A.A$
11.A.A$9.3A.2A83.2A$8.A88.A.A$9.3A.2A82.A$11.A.2A81.2A2$21.2A$21.2A7.
2A$30.A$28.A.A73.3D$28.2A75.D8.2A$105.3D6.A$115.3A$117.A$8.2A$8.2A2$
98.2A$97.A.A$97.A$24.A71.2A$23.A.A$23.A.A$24.A$25.3A$27.A2$106.2A$
106.2A7.2A$115.A$105.D7.A.A$104.3D6.2A$103.D2.2D2$99.2A$98.A.A$98.A$
97.2A2$36.2A3.2A27.A$36.2A3.2A25.3A$67.A$67.2A$29.2A$30.A$30.A.A$31.
2A82.2A$115.A.A$66.D3.2A15.D29.A$66.2D2.2A15.D.D27.2A$67.2D18.3D.2A$
67.D21.D.2A$66.D$34.2A$35.A$32.3A28.2A$32.A31.A50.2A$61.3A51.2A$61.A
27.2A$88.A.A$88.A$87.2A26.2A$115.2A$47.2A52.2A$47.2A51.A.A$39.2A59.A$
40.A6.3D49.2A8.2A$37.3A8.D60.A$37.A10.3D59.3A$112.A$38.A$37.A.A$37.A.
A$35.3A.2A$34.A$35.3A.2A$37.A.2A2$47.2A$47.2A7.2A$56.A$54.A.A$47.3A4.
2A$47.A$48.A2$34.2A$34.2A5$50.A$49.A.A$49.A.A$50.A$51.3A$53.A7$70.2A$
2.A67.A.A$A3.A65.A$5.A$A4.A71.2A$.5A71.2A3$74.2A$74.A.A$72.A.A.3A$72.
2A5.A$78.2A!


Orthogonoid444:
x = 123, y = 213, rule = LifeHistory
100.2A$100.2A11$114.2A$114.A.A$116.A$116.2A3$74.2C$73.C2.C$74.2C9.A
18.3D$58.D25.A.A8.2A8.D$56.D3.D24.2A9.A6.3D$55.D37.3A$55.D4.D32.A$55.
5D3$111.2E$111.E.E$113.E$113.2E6$74.2A$74.2A27.2A$94.2A7.2A$73.3D19.A
$74.D20.A.A7.D$72.3D21.2A6.3D$103.2D2.D2$114.2A$114.A$112.A.A$112.2A
3$98.2A$97.A.A$97.A$96.2A4$72.2A$63.2A7.2A$64.A45.3D$23.A40.A.A7.D26.
2A8.D$23.3A33.2A4.2A6.3D26.A6.3D$10.2A3.2A9.A17.A15.A11.2D2.D4.2A16.
3A$10.2A3.2A8.2A15.3A15.A.A18.A17.A$41.A19.2A16.A.A$41.2A36.2A$3.2A$
4.A112.2A$4.A.A110.A.A$5.2A85.2A25.A$93.A25.2A$40.D3.2A15.D31.A.A15.
2A$40.2D2.2A15.D.D30.2A15.2A$41.2D18.3D$41.D21.D$40.D$8.2A63.2A$9.A
63.2A2.2A$6.3A28.2A38.A.A$6.A31.A15.2A23.A$35.3A17.A23.2A$35.A16.3A$
52.A2$102.3D7.2A$103.D8.A.A$21.2A80.3D8.A$21.2A91.2A$13.2A$14.A6.3D$
11.3A8.D$11.A10.3D$96.2A$12.A82.A.A$11.A.A81.A25.2A$11.A.A80.2A25.A$
9.3A.2A87.2A15.A.A$8.A93.2A15.2A$9.3A.2A$11.A.2A2$21.2A$21.2A7.2A$30.
A$28.A.A$28.2A4$8.2A91.2A7.3D$8.2A90.A.A8.D$100.A8.3D$99.2A3$24.A$23.
A.A$23.A.A91.2A$24.A92.A.A$25.3A91.A$27.A91.2A7$109.2A$100.2A7.2A$
101.A$101.A.A7.D$102.2A6.3D$109.2D2.D4.2A$118.A$116.A.A$116.2A2$101.A
$101.3A$92.A11.A$42.2A3.2A27.A15.3A8.2A14.A$42.2A3.2A25.3A18.A22.A.A$
73.A20.2A16.D6.A$73.2A36.3D$35.2A74.D$36.A$36.A.A$37.2A2$72.D3.2A15.D
$72.2D2.2A15.D.D18.2A$73.2D18.3D18.A$73.D21.D11.2A6.3A$72.D34.A9.A$
40.2A66.3A$41.A68.A$38.3A28.2A$38.A31.A15.2A$67.3A17.A$67.A16.3A$84.A
4$53.2A$53.2A$45.2A$46.A6.3D$43.3A8.D$43.A10.3D2$44.A$43.A.A$43.A.A$
41.3A.2A$40.A$41.3A.2A$43.A.2A2$53.2A$53.2A7.2A$62.A$60.A.A$53.3C4.2A
$53.C$54.C2$40.2A$40.2A5$56.A$55.A.A$55.A.A$56.A$57.3A$59.A2$2.A$A3.A
$5.A62.2A$A4.A59.3A.2A6.2A$.5A59.5A7.2A$66.3A2$74.2A$74.A.A$72.A.A.3A
$72.2A5.A$78.2A!

I wouldn't be surprised if there's a more efficient option still out there somewhere. These first three designs were all found with manual searches. Notice that Orthogonoid446 adds an extra eater at the top to help clean up the extra beehive. No doubt there are lots of other ways to do that kind of thing.
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dvgrn
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Joined: May 17th, 2009, 11:00 pm
Location: Madison, WI

Re: Orthogonoid working notes

Postby simeks » June 7th, 2016, 2:46 pm

dvgrn wrote:Do you have lists of glider spacings handy, or should I just extract them from the RLE?

Yes, sorry, it's just that the format of the output has changes slightly...

- The first "0" represents the first glider, before the first number used to represent the second glider.
- Each new salvo starts with a "0" or "1", before it could be "90", "91", "254" or "255", and if it was "90" or "91" you couldn't be sure if it required exactly that timing or not. Now anything that isn't "0" or "1" need to be exactly timed.
- The timing is now relative to the "base timing" of the salvo, not to the previous glider. For example "1, 94" now means the second glider should be 93 ticks behind the first, and once that is supported by the program, a four glider salvo might be like "1, 94, 205, 301", meaning the fourth glider follows 96 ticks behind the third.

I'm attaching the raw output of this small xwss search. It also includes some more recipes that consumes the elbow:

xwss.zip
(28.94 KiB) Downloaded 159 times

I have also made a preliminary evaluation of small common patterns as elbows. The main conclusion is that any elbow that can be kept reasonably contained and that diversifies withing the first few gliders, will also give rise to good recipes. In particular the traffic light seems very useful - even more so than the pi-producing block. It can actually be placed anywhere within reach from the glider lane and still produce a multitude of recipes. Here's a first suggestion for a standard set of elbows, each shown with a glider-producing recipe:

x = 4999, y = 1655, rule = LifeHistory
995.D37.D$994.D2.3D.3D16.3D4.3D4.D$994.D3.D3.D16.D3.D2.D3.D3.D$993.D
4.D3.D.3D.3D3.D4.D3.D2.D3.D4.D$993.D4.5D2.D3.D4.D4.D3.D3.3D5.D$993.D
4.D3.D2.D3.D2.5D2.D3.D2.D3.D4.D$993.D4.D3.D3.D.D5.D4.D3.D2.D3.D4.D$
993.D4.D3.D3.D.D5.D4.D3.D2.D3.D4.D$994.D2.3D.3D3.D12.3D4.3D4.D$994.D
39.D$995.D37.D6$995.D44.D$994.D2.5D11.3D11.3D4.3D4.D$994.D3.D3.D3.D5.
D3.D9.D3.D2.D3.D3.D$993.D4.D3.D2.4D7.D4.D4.D3.D2.D3.D4.D$993.D4.4D4.D
8.D5.D4.D3.D3.3D5.D$993.D4.D3.D3.D7.D4.5D2.D3.D2.D3.D4.D$993.D4.D3.D
3.D6.D7.D4.D3.D2.D3.D4.D$993.D4.D3.D3.D2.D2.D8.D4.D3.D2.D3.D4.D$994.D
2.5D5.2D3.5D10.3D4.3D4.D$994.D46.D$995.D44.D6$995.D37.D$994.D2.5D6.2D
10.3D4.3D4.D$994.D3.D3.D6.D9.D3.D2.D3.D3.D$993.D4.D3.D3.2D.D4.D4.D3.D
2.D3.D4.D$993.D4.D3.D2.D2.2D4.D4.D3.D2.D3.D4.D$993.D4.4D3.D3.D2.5D2.D
3.D2.D3.D4.D$993.D4.D6.D3.D4.D4.D3.D2.D3.D4.D$993.D4.D6.D3.D4.D4.D3.D
2.D3.D4.D$994.D2.3D6.5D9.3D4.3D4.D$994.D39.D$995.D37.D7$997.5D2.2D14.
3D5.D96.3D.3D16.3D4.3D95.5D18.3D5.3D94.5D18.3D4.3D95.3D.9D10.3D7.D94.
3D.9D10.3D5.3D94.3D.9D10.3D3.5D94.3D.9D10.3D4.3D95.3D.9D11.D5.3D95.3D
.9D11.D6.D96.3D.9D11.D5.3D95.7D.3D6.D12.3D5.D89.7D.3D6.D12.3D4.3D88.
7D.3D6.D12.3D7.D87.7D.3D6.D12.3D5.3D87.7D.3D5.3D11.3D5.D89.7D.3D5.3D
11.3D4.3D88.7D.3D5.3D11.3D4.3D88.7D.3D5.3D11.3D7.D87.7D.3D5.3D11.3D3.
5D87.7D.3D5.3D11.3D4.3D88.7D.3D5.3D11.3D4.3D89.3D6.3D4.D12.3D5.D90.3D
6.3D3.3D12.D5.3D89.3D6.3D3.3D11.3D4.3D88.5D12.D12.3D4.3D88.5D11.3D11.
3D4.3D88.5D11.3D11.3D5.D89.5D11.3D11.3D4.3D88.9D14.3D4.3D95.5D6.2D10.
3D5.D96.5D6.2D10.3D4.3D$998.D3.D2.D13.D3.D3.2D97.D3.D16.D3.D2.D3.D95.
D3.D16.D3.D3.D98.D3.D16.D3.D2.D3.D95.D3.D2.D3.D9.D3.D5.2D95.D3.D2.D3.
D9.D3.D3.D98.D3.D2.D3.D9.D3.D2.D3.D95.D3.D2.D3.D9.D3.D2.D3.D95.D3.D2.
D3.D10.2D4.D3.D95.D3.D2.D3.D10.2D5.2D97.D3.D2.D3.D10.2D4.D3.D94.D2.D
2.D2.D6.2D11.D3.D3.2D89.D2.D2.D2.D6.2D11.D3.D2.D3.D87.D2.D2.D2.D6.2D
11.D3.D5.2D87.D2.D2.D2.D6.2D11.D3.D3.D90.D2.D2.D2.D5.D3.D9.D3.D3.2D
89.D2.D2.D2.D5.D3.D9.D3.D2.D3.D87.D2.D2.D2.D5.D3.D9.D3.D2.D3.D87.D2.D
2.D2.D5.D3.D9.D3.D5.2D87.D2.D2.D2.D5.D3.D9.D3.D2.D3.D87.D2.D2.D2.D5.D
3.D9.D3.D2.D3.D87.D2.D2.D2.D5.D3.D9.D3.D2.D3.D89.D6.D6.2D11.D3.D3.2D
91.D6.D5.D3.D10.2D4.D3.D89.D6.D5.D3.D9.D3.D2.D3.D88.D3.D3.D6.2D11.D3.
D2.D3.D88.D3.D3.D5.D3.D9.D3.D2.D3.D88.D3.D3.D5.D3.D9.D3.D3.2D90.D3.D
3.D5.D3.D9.D3.D2.D3.D87.D2.D2.D.D13.D3.D2.D3.D95.D3.D6.D9.D3.D3.2D97.
D3.D6.D9.D3.D2.D3.D$998.D3.D2.D.3D9.D3.D4.D97.D3.D.3D.3D8.D3.D6.D95.D
3.D2.2D.2D4.D4.D3.D2.D99.D3.D2.2D.2D4.D4.D3.D2.D3.D95.D3.D2.D.D6.D4.D
3.D4.D.D95.D3.D2.D.D6.D4.D3.D2.D99.D3.D2.D.D6.D4.D3.D6.D95.D3.D2.D.D
6.D4.D3.D2.D3.D95.D3.D2.D.D6.D6.D4.D3.D95.D3.D2.D.D6.D6.D6.D97.D3.D2.
D.D6.D6.D8.D97.D5.D7.D6.D4.D3.D4.D92.D5.D7.D6.D4.D3.D6.D90.D5.D7.D6.D
4.D3.D4.D.D90.D5.D7.D6.D4.D3.D2.D94.D5.D9.D4.D4.D3.D4.D92.D5.D9.D4.D
4.D3.D6.D90.D5.D9.D4.D4.D3.D6.D90.D5.D9.D4.D4.D3.D4.D.D90.D5.D9.D4.D
4.D3.D6.D90.D5.D9.D4.D4.D3.D2.D3.D90.D5.D9.D4.D4.D3.D2.D3.D89.D5.4D5.
D11.D3.D4.D91.D5.4D7.D4.D6.D4.D3.D89.D5.4D7.D9.D3.D6.D88.D3.D2.4D5.D
6.D4.D3.D2.D3.D88.D3.D2.4D7.D4.D4.D3.D2.D3.D88.D3.D2.4D7.D9.D3.D4.D
90.D3.D2.4D7.D4.D4.D3.D6.D90.D4.D.2D5.D4.D3.D6.D95.D3.D3.2D.D9.D3.D4.
D97.D3.D3.2D.D4.D4.D3.D6.D$998.4D3.D2.D10.D3.D4.D97.5D2.D3.D9.D3.D5.D
96.4D4.2D6.D4.D3.D2.4D96.4D4.2D6.D4.D3.D3.3D96.5D2.3D6.D4.D3.D3.D2.D
95.5D2.3D6.D4.D3.D2.4D96.5D2.3D6.D4.D3.D5.D96.5D2.3D6.D4.D3.D2.D3.D
95.5D2.3D6.D6.D4.D3.D95.5D2.3D6.D6.D6.D97.5D2.3D6.D6.D6.2D98.D5.D7.D
6.D4.D3.D4.D92.D5.D7.D6.D4.D3.D4.2D91.D5.D7.D6.D4.D3.D3.D2.D90.D5.D7.
D6.D4.D3.D2.4D91.D5.D8.D5.D4.D3.D4.D92.D5.D8.D5.D4.D3.D5.D91.D5.D8.D
5.D4.D3.D4.2D91.D5.D8.D5.D4.D3.D3.D2.D90.D5.D8.D5.D4.D3.D5.D91.D5.D8.
D5.D4.D3.D3.3D91.D5.D8.D5.D4.D3.D2.D3.D89.D6.D7.D11.D3.D4.D91.D6.D8.D
5.D6.D4.D3.D89.D6.D7.2D10.D3.D5.D89.4D4.D7.D6.D4.D3.D2.D3.D88.4D4.D8.
D5.D4.D3.D2.D3.D88.4D4.D7.2D10.D3.D4.D90.4D4.D7.2D5.D4.D3.D5.D91.D4.
2D2.D4.D4.D3.D5.D96.D3.D2.D2.2D9.D3.D4.D97.D3.D2.D2.2D4.D4.D3.D4.2D$
998.D3.D2.3D4.5D2.D3.D4.D97.D3.D2.D3.D2.5D2.D3.D4.D97.D3.D3.D5.5D2.D
3.D2.D3.D95.D3.D3.D5.5D2.D3.D2.D3.D95.D3.D2.D.D4.5D2.D3.D2.D3.D95.D3.
D2.D.D4.5D2.D3.D2.D3.D95.D3.D2.D.D4.5D2.D3.D5.D96.D3.D2.D.D4.5D2.D3.D
3.4D95.D3.D2.D.D4.5D4.D4.D3.D95.D3.D2.D.D4.5D4.D6.D97.D3.D2.D.D4.5D4.
D8.D97.D5.D7.D4.5D2.D3.D4.D92.D5.D7.D4.5D2.D3.D6.D90.D5.D7.D4.5D2.D3.
D2.D3.D90.D5.D7.D4.5D2.D3.D2.D3.D90.D5.D7.D4.5D2.D3.D4.D92.D5.D7.D4.
5D2.D3.D4.D92.D5.D7.D4.5D2.D3.D6.D90.D5.D7.D4.5D2.D3.D2.D3.D90.D5.D7.
D4.5D2.D3.D5.D91.D5.D7.D4.5D2.D3.D2.D3.D90.D5.D7.D4.5D2.D3.D3.4D89.D
6.D7.D4.5D2.D3.D4.D91.D6.D7.D4.5D4.D4.D3.D89.D6.D9.D2.5D2.D3.D4.D90.D
3.D3.D7.D4.5D2.D3.D2.D3.D88.D3.D3.D7.D4.5D2.D3.D2.D3.D88.D3.D3.D9.D2.
5D2.D3.D4.D90.D3.D3.D9.D2.5D2.D3.D4.D92.D4.D3.D2.5D2.D3.D4.D97.4D3.D
3.D2.5D2.D3.D4.D97.4D3.D3.D2.5D2.D3.D6.D$998.D3.D2.D.D11.D3.D4.D97.D
3.D3.D.D10.D3.D3.D98.D3.D3.D7.D4.D3.D2.D3.D95.D3.D3.D7.D4.D3.D2.D3.D
95.D3.D2.D8.D4.D3.D2.6D94.D3.D2.D8.D4.D3.D2.D3.D95.D3.D2.D8.D4.D3.D4.
D97.D3.D2.D8.D4.D3.D6.D95.D3.D2.D8.D6.D4.D3.D95.D3.D2.D8.D6.D6.D97.D
3.D2.D8.D6.D8.D97.D5.D2.D4.D6.D4.D3.D4.D92.D5.D2.D4.D6.D4.D3.D6.D90.D
5.D2.D4.D6.D4.D3.D2.6D89.D5.D2.D4.D6.D4.D3.D2.D3.D90.D5.D2.D3.D7.D4.D
3.D4.D92.D5.D2.D3.D7.D4.D3.D3.D93.D5.D2.D3.D7.D4.D3.D6.D90.D5.D2.D3.D
7.D4.D3.D2.6D89.D5.D2.D3.D7.D4.D3.D4.D92.D5.D2.D3.D7.D4.D3.D2.D3.D90.
D5.D2.D3.D7.D4.D3.D6.D89.D2.D3.D7.D11.D3.D4.D91.D2.D3.D6.D7.D6.D4.D3.
D89.D2.D3.D9.D9.D3.D3.D91.D3.D3.D7.D6.D4.D3.D2.D3.D88.D3.D3.D6.D7.D4.
D3.D2.D3.D88.D3.D3.D9.D9.D3.D4.D90.D3.D3.D9.D4.D4.D3.D3.D93.D4.D3.D4.
D4.D3.D3.D98.D6.D3.D9.D3.D4.D97.D6.D3.D4.D4.D3.D6.D$998.D3.D2.D2.D10.
D3.D4.D97.D3.D3.D.D10.D3.D2.D99.D3.D3.D7.D4.D3.D2.D3.D95.D3.D3.D7.D4.
D3.D2.D3.D95.D3.D2.D8.D4.D3.D6.D95.D3.D2.D8.D4.D3.D2.D3.D95.D3.D2.D8.
D4.D3.D4.D97.D3.D2.D8.D4.D3.D5.D96.D3.D2.D8.D6.D4.D3.D95.D3.D2.D8.D6.
D6.D97.D3.D2.D8.D6.D4.D3.D97.D5.D2.D4.D6.D4.D3.D4.D92.D5.D2.D4.D6.D4.
D3.D2.D3.D90.D5.D2.D4.D6.D4.D3.D6.D90.D5.D2.D4.D6.D4.D3.D2.D3.D90.D5.
D2.D2.D8.D4.D3.D4.D92.D5.D2.D2.D8.D4.D3.D2.D94.D5.D2.D2.D8.D4.D3.D2.D
3.D90.D5.D2.D2.D8.D4.D3.D6.D90.D5.D2.D2.D8.D4.D3.D4.D92.D5.D2.D2.D8.D
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127.2A126.2A126.A126.2A127.2A126.2A126.A127.2A126.2A$1013.2A126.A.A
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A126.3A125.3A125.3A125.3A125.3A125.3A125.3A242.A$1008.2A252.A1162.A
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127.A128.A382.3A124.A$1139.A391.A127.A127.A127.A127.A127.A127.A1269.
2A125.3A128.A256.A766.A$1138.A1663.2A637.3A124.A.A127.A127.A256.A766.
A$2675.2A124.A.A511.2A126.A126.A126.A$2289.3A255.3A124.A.A126.A256.2A
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125.3A126.A126.A126.A257.A511.A$1526.2A124.A.A127.A125.A$1525.A.A126.
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1220.2A1168.A375.3A511.3A763.A504.A.A$1219.A1548.A513.A1527.A$2767.A
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2A$1954.A.A127.A124.A257.A386.A252.A$1573.2A381.A126.A769.A$1446.2A
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1167.3A1783.A378.2A$1273.A.A528.3A377.3A258.A509.3A1396.3A252.2A$
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$2335.3A1912.A506.3A$2337.A123.2A384.2A1400.A509.A$1569.2A765.A123.A.
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257.3A1514.2A391.A.A511.A.A$1863.2A258.A1513.A.A907.A$1862.A.A257.A
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256.3A1514.A$1702.A.A258.A1514.2A$1704.A257.A1514.A.A$3739.A$3102.A
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3A$1178.2A2036.A$1177.A377.A510.3A1146.A$1555.2A511.A$1554.A.A510.A
1387.2A$1046.2A631.2A1773.A.A904.3A$1045.A.A630.A.A894.2A879.A906.A$
1047.A632.A895.2A1784.A$2575.A$1933.2A$1934.2A$1933.A1015.2A$2948.A.A
$2950.A759.2A$3711.2A124.A638.A$3710.A126.2A637.2A$3836.A.A250.3A383.
A.A$4091.A$4090.A$2302.2A$2301.A.A1656.A$2303.A1656.2A$3959.A.A$499.
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A780.A.A894.3A1778.A$1532.A896.A$1401.2A1025.A$1400.A.A$1402.A2$3566.
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116.2A125.2A1934.A.A1012.2A$609.A115.A.A124.A.A2950.2A378.A$608.A118.
A3076.A380.2A$2658.2A1524.A.A$1759.2A896.A.A$1760.2A897.A$1759.A$
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$1368.2A$1367.A.A$3022.2A$3021.A.A$3023.A2$2766.2A$2765.A.A$2767.A2$
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2A630.A.A894.2A879.A905.2A$965.A.A632.A895.2A1783.A$2495.A$1853.2A$
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3A$1644.A.A768.3A127.A748.A.A906.A$1646.A770.A1784.A$2416.A$1773.2A$
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381.2A$979.A509.A382.2A$979.2A890.A$978.A.A3309.2A$4291.2A$4290.A3$
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$2062.2A514.A1012.3A$2061.A.A513.A1015.A$3592.A$3970.2A$3971.2A$3970.
A$1291.2A$1290.A.A1148.2A$1292.A1147.A.A$2442.A2$628.2A2441.3A$629.2A
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3891.A2$2361.A$2361.2A$2360.A.A2$2991.3A$2993.A$2861.2A129.A$2862.2A$
2861.A$1328.2A$1327.A.A$1329.A3$412.2A$411.A.A$413.A2183.2A$2596.A.A$
686.A1911.A$686.2A2405.A$685.A.A2405.2A$2213.3A876.A.A$2215.A1648.2A$
2214.A1138.2A508.A.A$1186.A2165.A.A510.A$1186.2A2166.A$1185.A.A1147.
2A$2334.A.A631.2A$2336.A632.2A$2968.A$2837.2A635.A$1943.2A891.A.A635.
2A$1305.3A634.A.A893.A634.A.A$1307.A636.A$1306.A$1048.2A$1047.A.A
2166.2A$1049.A2167.2A$3216.A4$788.2A3311.2A$789.2A3309.A.A$788.A3313.
A$262.3A$264.A$263.A3$1671.2A$1670.A.A$1672.A3$649.2A$648.A.A$650.A$
1405.2A383.2A$1024.3A377.A.A382.A.A$1026.A379.A384.A1400.3A$1025.A
2168.A$3193.A$1147.A$1147.2A$765.3A378.A.A$767.A$766.A$2672.2A$2038.
2A631.A.A$2037.A.A633.A$2039.A8$228.2A$227.A.A$229.A4$1763.2A$1377.2A
385.2A$1378.2A383.A$1377.A6$332.2A$331.A.A$333.A3$3013.2A$3012.A.A$
2133.2A879.A$2134.2A1648.2A$2133.A1649.A.A$3785.A2$2255.2A$2254.A.A
631.3A$2256.A633.A$2889.A$2757.A636.A$1863.2A892.2A635.2A$1225.3A634.
A.A891.A.A634.A.A$1227.A636.A$1226.A6$306.3A$308.A$307.A3713.2A$4020.
A.A$2110.A1911.A$2110.2A$2109.A.A9$569.A$569.2A$568.A.A$1199.3A$944.
3A254.A$946.A253.A1911.3A$945.A2168.A$3113.A$1067.A$1067.2A$685.3A
378.A.A$687.A$686.A2$1958.2A$1957.A.A2033.2A$1959.A2032.A.A$3994.A7$
545.2A$546.2A$545.A5$1297.3A$1299.A$1298.A3$3081.3A$1038.3A2042.A$
1040.A2041.A$1039.A2$654.A$654.2A$653.A.A$2933.2A$1927.A1004.A.A$
1927.2A1005.A$1926.A.A1775.2A$3703.A.A$3705.A3$2808.3A$2810.A$2809.A$
2677.A636.2A$1783.2A892.2A634.A.A$1782.A.A891.A.A636.A$1784.A7$226.3A
$228.A$227.A2$2030.2A$2029.A.A$2031.A12$1119.3A$864.2A255.A$865.2A
253.A$864.A2$3663.2A$3664.2A$3663.A2$2768.3A$2770.A$2769.A$3913.2A$
3912.A.A$3914.A4$1998.2A$1997.A.A$1999.A$465.3A$467.A$466.A629.3A$
1098.A$1097.A3$1217.3A$1219.A$1218.A4$958.3A$960.A$959.A2$574.A$574.
2A$573.A.A2$1847.2A$1846.A.A$1848.A8$2597.2A$2596.A.A$2598.A8$146.2A$
147.2A$146.A12$916.2A$917.2A$916.A3$784.3A$786.A$785.A2$3583.3A$3585.
A$3584.A2$2688.3A$2690.A$2689.A7$110.2A$109.A.A$111.A$385.3A$387.A$
386.A5$1137.2A$1138.2A$1137.A$754.A$754.2A$753.A.A5$494.A$494.2A$493.
A.A2$1767.A$1767.2A$1766.A.A8$2517.2A$2516.A.A$2518.A10$1101.A$1101.
2A$1100.A.A19$3503.3A$3505.A$3504.A2$2608.3A$2610.A$2609.A10$305.3A$
307.A$306.A7$3478.2A$3477.A.A$3479.A6$414.A$414.2A$413.A.A$2576.3A$
1687.2A889.A$1686.A.A888.A$1688.A17$265.3A$267.A$266.A$1021.2A$1020.A
.A$1022.A52$334.2A$333.A.A$335.A2$1607.A$1607.2A$1606.A.A17$185.3A$
187.A$186.A22$1564.2A$1565.2A$1564.A31$254.A$254.2A$253.A.A21$105.2A
124.A$106.2A123.2A$105.A124.A.A78$25.3A$27.A$26.A23$3A$2.A$.A!
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Re: Orthogonoid working notes

Postby dvgrn » June 7th, 2016, 6:54 pm

simeks wrote:- The first "0" represents the first glider, before the first number used to represent the second glider.
- Each new salvo starts with a "0" or "1"...

This looks great -- the raw output format does a great job of providing all the information that anyone could possibly want, and it's easy to cut it down and find the pieces I might really need.

I won't bother updating my temporary optimizer script to match this new format, since it looks like you're pretty close to providing all that information already. Here are a few questions, though.

I'm understanding recipes like this:
/* -99, gl=2,-10 */ { 0, 109, 1, 94, 1, 0, 153, 0, 0, 1, 101, 1, 105, 0, 0, 91, 1, 98, 0, -1},
/* -99, gl=2,-10 */ {0,109; 1,94; 1; 0,153; 0; 0; 1,101; 1,105; 0; 0,91; 1,98; 0; -1 just means "the end".}

1) Aren't there situations where you start a group of glider timings with a "0" or a "1", but there's not really a completely free choice about when the next glider can arrive? If a reaction takes a long time to settle, then you might not be able to send the next following glider at +90 or +91 ticks; maybe the minimum safe distance would be +100 or +200 or +300 ticks.

My script gave a follow-distance rating for each recipe it optimized, just one more number added at the end of the optimized recipe. Maybe you could include that information in your recipes somehow? One way I thought of that would keep the recipes as nice simple lists of integers, would be to add a negative number after each group. "-250" would mean that any following distance greater than 250 ticks would be okay.

2) Could there be a distinction between two possible ways to start the next series of gliders?

"1" is unambiguous -- "next glider's parity must be odd".

But "0" for the next glider's parity could mean either "must be even" (if the current target is P2) or "can be even" (current target is P1, so this would be an opportunity to change parity for any gliders or spaceships emitted after this point). It would be nice to be able to tell the difference between those two cases, without having to re-run each recipe and classify all the intermediate targets.
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Re: Orthogonoid working notes

Postby simeks » June 8th, 2016, 12:39 pm

dvgrn wrote:I won't bother updating my temporary optimizer script to match this new format, since it looks like you're pretty close to providing all that information already. Here are a few questions, though.

This is not really the case, I was not trying to generate all information your script can, the improved information is just a side-effect of a slightly different search order:

For example, when generating stable patterns that can be reached from 15 gliders, I now first generate patterns by adding one glider to stable patterns reached from 14 gliders, and after that I add two gliders to patterns reached from 13 gliders. In the process, any new stable pattern that has been seen anytime before is detected from a hashtable look-up, and ignored.

The net result is that if there is a way to generate a stable pattern from independent gliders it will be found first, and other ways to generate the same pattern are then discarded.

So to answer the rest of your post, I think all things you mention are true, but I was hoping your script would take care of those ;)
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Re: Orthogonoid working notes

Postby dvgrn » June 9th, 2016, 9:22 pm

simeks wrote:This is not really the case, I was not trying to generate all information your script can, the improved information is just a side-effect of a slightly different search order...
So to answer the rest of your post, I think all things you mention are true, but I was hoping your script would take care of those ;)

Okay, I can probably make the adjustments for the new format pretty easily, maybe this weekend. And I'll see about collecting the rest of the information at the same time. Was thinking that P1 intermediate elbows should be followed by a "0", P2 elbows requiring an odd-parity glider should get a "1", and P2 elbows requiring an even-parity glider would get a "2".

I probably shouldn't get too distracted, but I'm still interested in finding out if it's possible to line up gaps between single-channel gliders reliably to let construction gliders through, for a square Orthogonoid design. Will probably try a script to build a sample blueprint with adjustable vertical spacing, horizontal spacing, and standard distances between single-channel glider groups, just to see if the math can be made to work out.
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Re: Orthogonoid working notes

Postby dvgrn » September 3rd, 2016, 4:23 pm

dvgrn wrote:
simeks wrote:I probably shouldn't get too distracted, but I'm still interested in finding out if it's possible to line up gaps between single-channel gliders reliably to let construction gliders through, for a square Orthogonoid design. Will probably try a script to build a sample blueprint with adjustable vertical spacing, horizontal spacing, and standard distances between single-channel glider groups, just to see if the math can be made to work out.

Haven't done the script yet, but it seems pretty clear that slow-salvo construction gliders will be able to fire through gaps in the single-channel recipe stream -- if the distances between pairs of gliders (or triplets, quadruplets, etc., if we include those in recipes) are just made large enough, and timed correctly.

A few weeks ago I did a little more research for a highly Hashlife-compatible Orthogonoid replicator unit design. Without spending a few weeks fixing up Hersrch's data, here's the best I could manage:

x = 472, y = 355, rule = LifeHistory
93.A$92.A.A$92.A.A$91.2A.3A$92.B4.A$90.B2AB3A$90.B2A.A$89.2B$80.3B2D
6B$74.2A5.2B2D6B$75.A5.10B$75.A.AB2.11B$76.2AB.2B3D7B$78.6BD8B$78.5BD
10B$78.16B.2B$78.18B2A$77.17B.B2A$76.4B2.8B.4B.B$75.4B4.7B$74.4B5.6B$
73.4B6.4B$72.4B5.A3B$71.4B5.A.AB$70.4B6.A.A$69.4B8.A$68.4B6.3A$67.4B
7.A$66.4B$65.4B$64.4B$63.4B$62.4B$61.4B$60.4B$59.4B$58.4B$57.4B$56.4B
$55.4B$54.4B$53.4B414.B$52.4B414.2B$51.4B414.3B$50.4B414.4B$49.4B414.
4B$48.4B414.4B$47.4B414.4B$46.4B414.4B$45.4B414.4B$44.4B414.4B$43.4B
414.4B$42.4B414.4B$41.4B414.4B$40.4B414.4B$39.4B414.4B$38.4B414.4B$
37.4B414.4B$36.4B414.4B$35.4B414.4B$34.4B414.4B$33.4B414.4B$32.4B396.
2A16.4B$31.4B396.B2AB14.4B$30.4B391.B6.2B14.4B$29.4B391.3B4.2B14.4B$
28.4B388.14B12.4B$27.4B389.14B11.4B$26.4B390.17B5.B.4B$25.4B390.28B$
24.4B389.30B$23.4B389.31B$22.4B389.32B$21.4B389.32B$20.4B389.4B3.23B
2.B2A$19.4B389.4B7.16B.B4.BA.A$18.4B389.4B9.2B.10B11.A$17.4B379.A9.4B
13.9B12.2A$16.4B380.3A6.4B15.11B$15.4B384.A4.4B16.12B$14.4B384.2AB2.
4B17.12B$13.4B385.8B19.11B$12.4B388.6B17.4B.4B3DB$11.4B389.7B16.2A4.
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16BABA16.8B$5.382BD3BD24B2A17.8B$2.B.382BD30B18.9B$.2A383BD4BD23B19.
6B.4B$.2A383B5D25B18.7B.4B$2.B2.411B19.6B2.4B$4.2B2.B.B.B.B.B.B.B.B.B
.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.
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B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.16B19.6B3.4B$4.2AB395.14B19.6B4.4B$3.A.
A396.13B19.8B4.4B$.3A.A.A394.11B20.8B6.4B$A5.2A393.13B19.9B6.4B$2A
398.15B18.9B7.4B$399.16B17.10B8.4B$398.17B17.3B2A5B9.4B$399.16B16.4B
2A5B10.4B$400.13B18.11B11.4B$400.5B2A2B20.A7BD4B12.4B$402.3B2A2B18.3A
2.4B3DB15.4B$402.8B16.A6.2B2D2BD16.4B$401.3B3D2B17.2A6.6B17.4B$401.4B
D3B25.7B17.4B$401.2B3D2B25.7B5.2A12.4B$401.7B25.8B3.A.A13.4B$402.6B
25.8B3.A16.4B$402.6B25.9B.2A17.4B$403.5B24.11B20.4B$403.6B22.12B21.4B
$402.6B23.12B22.4B$402.7B15.2A6.10B24.4B$386.2A15.6B16.A7.11B23.4B$
387.A8.B4.8B16.A.AB.14B24.4B$387.A.AB3.4B.6B2AB18.2AB.13B2A24.3B$388.
2AB.13B2A2B19.15B2A25.2B$390.18B19.15B.B27.B$390.17B21.14B$391.13B22.
2AB.11B$393.12B20.A.AB3.9B$395.10B20.A8.8B$395.11B18.2A9.7B$396.2B.7B
26.11B$396.11B24.12B$395.11B25.12B$395.11B25.11B$395.11B25.B3D4B.4B$
395.B3D4B2.B2A23.2BD4B4.2A$395.2BD4B3.BA.A22.2B3D2B4.A$395.2B3D2B6.A
22.6B6.3A$395.6B7.2A20.7B8.A$394.7B28.8B$393.8B27.8B$392.8B28.8B$392.
8B26.2AB2.6B$390.2AB2.6B24.A.AB.7B$389.A.AB.7B24.A4.6B$389.A4.6B24.2A
4.6B$388.2A4.6B30.6B$394.6B29.8B$393.8B29.8B$394.8B27.9B$393.9B27.9B$
393.9B27.10B$393.10B26.5B2A3B$393.5B2A3B26.5B2A4B3.2A$387.A5.5B2A4B3.
2A20.11B3.A$341.A45.3A3.11B3.A21.4BD7BA.A$341.3A34.A11.A2.4BD7BA.A23.
B3D4B2.2A$328.2A3.2A9.A17.A15.3A8.2A4.B3D4B2.2A24.D2B2D2B$327.B2AB.B
2AB7.2A15.3A18.A7.6BD2B2D2B29.5B$328.2B2.3B3.B4.4B12.A20.2A3.B5.10B
22.2A5.6B$329.3B.3B.4B4.3B11.2A19.8B2.11B23.A6.6B$321.2A5.7B.13B11.B
21.19B23.A.AB2.8B$322.A5.23B9.3B19.20B2A21.2AB2.9B$322.A.AB.19B.8B4.
6B16.21B2A23.12B$323.2AB.29B2.10B11.25B23.12B$325.44B3.2B2.26B25.10B.
B2A$325.33BD3B2A15BD14B4.4B26.8B2.BA.A$325.33B2D2B2A15BDBD4B.6B6.B.B
2A.A21.8B6.A$326.33B2D18B3D4B2.B.5B6.B2AB3A20.8B5.2A$328.31BD21BD4B7.
2A8.B4.A20.7B$326.32BD26B8.A8.2A.3A18.11B$326.2A3.25B4.13B.4B16.3A6.A
.A19.12B$327.A3.20B4.B4.7B.B5.3B19.A6.A.A19.12B$324.3A6.15B7.2A15.4B
28.A20.11B$324.A8.11B12.A15.2A51.B3D4B.4B$332.13B8.3A17.A51.2BD4B4.2A
$331.15B7.A16.3A52.2B3D2B4.A$331.16B23.A54.6B6.3A$331.17B76.7B8.A$
331.16B76.8B$333.13B76.8B$333.3B.2B2A5B76.8B$331.4B2.2B2A3B76.2AB2.6B
$331.2A3.8B75.A.AB.7B$332.A4.2B3D3B74.A4.6B15.2A$329.3A5.3BD4B73.2A4.
8B4.B8.A$329.A8.2B3D2B80.B2A6B.4B3.BA.A$338.7B79.2B2A13B.B2A$330.A7.
6B81.18B$329.A.A6.6B82.17B$329.A.A6.5B86.13B$327.3A.2A4.6B85.12B$326.
A4.B6.6B84.10B$327.3AB2AB3.7B83.11B$329.A.2AB.8B84.7B.2B$333.10B83.
11B$333.6B2A3B83.11B$333.6B2A2B5.2A77.11B$333.10B5.A78.11B$332.11B2.B
A.A76.2AB2.4B3DB$332.12B.B2A76.A.AB3.4BD2B$331.15B78.A6.2B3D2B$330.
16B77.2A7.6B$327.2B.16B86.7B$326.2A18B86.8B$326.2AB.17B86.8B$327.B.4B
.8B2.4B85.8B$334.7B4.4B83.6B2.B2A$335.6B5.4B82.7B.BA.A$337.4B6.4B82.
6B4.A$339.3BA5.4B81.6B4.2A$340.BA.A5.4B80.6B$341.A.A6.4B78.8B$342.A8.
4B76.8B$343.3A6.4B75.9B$345.A7.4B74.9B$354.4B72.10B$355.4B71.3B2A5B$
356.4B64.2A3.4B2A5B$357.4B64.A3.11B$358.4B63.A.A7BD4B$359.4B63.2A2.4B
3DB$360.4B67.2B2D2BD4.2A$361.4B67.6B4.A$362.4B66.6B.BA.A$363.4B64.7B.
B2A$364.4B58.A5.8B$365.4B57.3A3.7B$366.4B33.2A24.A2.7B$354.2A3.2A6.4B
17.A15.A13.2A6.3A2.7B4.B$353.B2AB.B2AB6.4B14.3A15.A.AB9.B2A2B4.A5.6B.
B.2BA$354.2B2.3B3.B4.4B12.A19.2AB.3B6.4B.3B5.11BA.A$355.3B.3B.4B3.4B
11.2A20.7B2.11B4.5BD4B.BA$347.2A5.7B.13B11.B20.22B.B.3B3D3B$348.A5.
23B9.3B19.24BD2BD5B$348.A.AB.19B.8B4.6B16.26BD7B$349.2AB.29B2.10B11.
28B2D6B$351.44B3.2B2.30B2D6B$351.33BD3B2A15BD26BD7B$351.33B2D2B2A15BD
BD4B.24B.3B$352.33B2D18B3D4B2.16B2.B.B3.B2A$354.31BD21BD4B2.7B.4B6.B
2AB2.BA.A$352.32BD26B4.6B2.2B8.2A4.B2A$352.2A3.25B4.13B.4B11.6B16.4B$
353.A3.20B4.B4.7B.B5.3B13.3B18.2A$350.3A6.15B7.2A15.4B12.7B17.A$350.A
8.11B12.A15.2A14.2A.B.2A14.3A$358.13B8.3A17.A15.A3.A15.A$357.15B7.A
16.3A13.3A5.3A$357.16B23.A15.A9.A$357.17B$357.16B$359.13B$359.3B.2B2A
5B$357.4B2.2B2A3B$357.2A3.8B$358.A4.2B3D3B$355.3A5.3BD4B$355.A8.2B3D
2B$364.7B$356.A7.6B$355.A.A6.6B$355.A.A6.5B$353.3A.2A4.6B$352.A4.B6.
6B$353.3AB2AB3.7B$355.A.2AB.8B$359.10B$359.6B2A3B$359.6B2A2B5.2A$359.
10B5.A$358.11B2.BA.A$358.7B3C2B.B2A$357.8BC6B$356.10BC5B$353.2B.16B$
352.2A18B$352.2AB.17B$353.B.4B.8B2.4B$360.7B4.4B$361.6B5.4B$363.4B6.
4B$365.3BA5.4B$366.BA.A5.4B$367.A.A6.4B$368.A8.4B$369.3A6.4B$371.A7.
4B$380.4B$381.4B$382.4B$383.4B$384.4B$385.4B$386.2B2C$387.BCBC$388.C
3B$388.B.3B$390.4B$391.4B$392.4B$393.4B$394.4B$395.4B$396.4B$397.4B$
398.4B$399.4B$400.4B$401.4B$402.4B$403.4B$404.4B$405.4B$406.4B$407.4B
$408.4B$409.4B$410.4B$411.4B$412.4B$413.4B$414.4B$415.4B$416.4B$417.
4B$418.4B$419.4B$420.4B$421.4B$422.4B$423.4B$424.4B$425.4B$426.4B$
427.4B$428.4B$429.4B$430.4B$431.4B$432.4B$433.4B$434.4B$435.4B$436.4B
$437.4B$438.4B$372.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.
B.B.B.B.B.B.B.B.5B$370.B.73B$372.74B.B$370.77B2A$371.76B2A$371.74B2.B
$373.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.
B.B.B2.2B$443.B2A$444.A.A$442.A.A.3A$442.2A5.A$448.2A!

The circuit recovers safely in 90 ticks, there are only three eater2s, vertical offset is 256 cells, and a glider gets from one replicator unit to the next in a power-of-two time. With a lot of these built into a rectangle that's something close to square, this should be by far the self-constructing spaceship with the smallest long diameter.

It will also travel surprisingly fast (as these things go) especially if it's made longer and thinner. The only required task for the first replicator unit is to build new target "elbow" and "hand" blocks at (0,-256) from their initial locations, while leaving viable copies near the old locations. All other construction can be done by replicator unit #2 and later.

I'd like to come up with a version of this that will allow a 128-cell vertical offset, since that will make the top speed much faster. Seems worth spending some time looking for.

-- Of course it doesn't matter in theory if the design allows a power-of-two temporal period; the spaceship will still be a spaceship if it's based on something like Orthogonoid444, above. But I think this might be a case where we'll need to keep the number of hashtiles to a minimum if we really want Golly to be able to run the pattern well; otherwise there will be too many different ways for the back-and-forth data *WSSes to line up.
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dvgrn
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Re: Orthogonoid working notes

Postby dvgrn » November 13th, 2016, 3:10 am

dvgrn wrote:The circuit recovers safely in 90 ticks, there are only three eater2s, vertical offset is 256 cells, and a glider gets from one replicator unit to the next in a power-of-two time. With a lot of these built into a rectangle that's something close to square, this should be by far the self-constructing spaceship with the smallest long diameter.
...
I'd like to come up with a version of this that will allow a 128-cell vertical offset, since that will make the top speed much faster. Seems worth spending some time looking for.

Okay, how about this one? Allow me to introduce Orthogonoid496:

x = 649, y = 559, rule = LifeHistory
99.A$97.3A$96.A26.A$96.2A25.3A$126.A$125.2A2$56.A49.A$40.A15.3A47.3A
40.2A$38.3A18.A49.A39.A$37.A20.2A11.2A11.D23.2A11.2A11.D12.A.A$37.2A
32.2A9.3D36.2A9.3D12.2A4.2A$82.D.D47.D.D18.A$82.D49.D18.A.A$14.2A4.2A
129.2A$14.2A3.A2.A$20.2A$36.D3.2A15.D49.D$36.2D2.2A15.D.D47.D.D41.2A$
37.2D18.3D36.2A9.3D41.A.A$37.D21.D23.2A11.2A11.D22.2A19.A$36.D47.A46.
A.A19.2A$81.3A47.A$15.2A64.A48.2A10.2A$15.2A4.D121.A$20.3D27.2A48.2A
38.3A$19.D2.2D27.A49.A38.A$48.3A20.2A25.3A20.2A$48.A22.A26.A22.A$12.
2A58.3A47.3A$12.A.A59.A49.A$14.A$14.2A148.2C$163.C2.C$154.A9.2C$153.A
.A$33.2A118.2A$33.A$31.A.A$14.2A15.2A$14.2A3$31.2A$31.A.A68.A$33.A66.
3A$33.2A64.A$89.2A8.2A$90.A$58.2A11.A18.A.A$58.2A10.A.A18.2A$24.3D43.
A.A32.2A57.2A$15.2A8.D43.2A.3A2.2A26.2A57.2A$16.A6.3D49.A2.A$13.3A53.
2A.3A3.A.A83.3D$13.A55.2A.A6.2A84.D$105.2A58.3D$105.2A2$31.2A$31.A.A$
33.A$33.2A31.2A11.D.2A$66.2A9.3D.2A$51.2A24.D.D27.2A$50.A2.A23.D29.A$
49.A.2A52.A.A$49.A55.2A$48.2A$23.2A38.2A$14.2A7.2A38.A$15.A48.3A$15.A
.A7.D40.A99.2A$16.2A6.3D139.2A7.2A$23.2D2.D147.A$165.D7.A.A$87.2A75.
3D6.2A$88.A74.D2.2D$56.2A3.2A25.A.A$56.2A3.2A26.2A31.A15.A9.A$122.3A
13.3A5.3A$93.D2.2D27.A15.A3.A$68.2A24.3D27.2A14.2A3.2A$68.A20.2A4.D$
66.A.A20.2A$66.2A$110.D$32.D78.D21.D$21.A9.2D78.2D18.3D$20.A.A7.2D78.
2D2.2A15.D.D$20.A.A8.D78.D3.2A15.D26.D$21.A10.D61.2A62.2D9.A$63.2A23.
2A3.A2.A62.2D7.A.A$63.A24.2A4.2A63.D8.A.A$29.2A3.2A28.3A91.D10.A$20.
2A7.2A3.A31.A$20.2A13.3A73.2A$37.A73.A19.2A27.2A$112.3A15.A.A11.2A6.A
7.2A7.2A$114.A15.A13.2A6.3A14.2A$129.2A24.A$154.2A$50.2A$50.2A$58.2A$
49.3D6.A$50.D8.3A$48.3D10.A2$60.A$59.A.A$59.A.A$58.2A.3A$64.A$58.2A.
3A$58.2A.A2$50.2A$41.2A7.2A$42.A$42.A.A$43.2A4$63.2A$63.2A2$549.A$
549.3A$525.A26.A$48.A474.3A25.2A$47.A.A472.A$47.A.A472.2A$48.A$45.3A
494.A49.A$45.A452.2A40.3A47.3A15.A$499.A39.A49.A18.3A$499.A.A12.D11.
2A11.2A23.D11.2A11.2A20.A$494.2A4.2A12.3D9.2A36.3D9.2A32.2A$495.A18.D
.D47.D.D$495.A.A18.D49.D$496.2A129.2A4.2A$626.A2.A3.2A$627.2A$541.D
49.D15.2A3.D$496.2A41.D.D47.D.D15.2A2.2D$495.A.A41.3D9.2A36.3D18.2D$
495.A19.2A22.D11.2A11.2A23.D21.D$494.2A19.A.A46.A47.D$517.A47.3A$505.
2A10.2A48.A64.2A$505.A121.D4.2A$506.3A38.2A48.2A27.3D$508.A38.A49.A
27.2D2.D$526.2A20.3A25.2A20.3A$527.A22.A26.A22.A$524.3A47.3A58.2A$
524.A49.A59.A.A$634.A$483.2C148.2A$482.C2.C$483.2C9.A$77.D415.A.A$75.
D3.D414.2A118.2A$29.5D40.D540.A$.2A26.D4.D39.D4.D535.A.A$.2A26.D44.5D
537.2A15.2A$30.D3.D598.2A$32.D$4.2A$3.A.A610.2A$.3A.A.A538.A68.A.A$A
5.2A538.3A66.A$2A547.A64.2A$548.2A8.2A$558.A$556.A.A18.A11.2A$556.2A
18.A.A10.2A$483.2A57.2A32.A.A43.3D$483.2A57.2A26.2A2.3A.2A43.D8.2A$
570.A2.A49.3D6.A$482.3D83.A.A3.3A.2A53.3A$483.D84.2A6.A.2A55.A$481.3D
58.2A$542.2A2$616.2A$615.A.A$615.A$566.2A.D11.2A31.2A$566.2A.3D9.2A$
540.2A27.D.D24.2A$541.A29.D23.A2.A$541.A.A52.2A.A$542.2A55.A$599.2A$
584.2A38.2A$585.A38.2A7.2A$582.3A48.A$481.2A99.A40.D7.A.A$472.2A7.2A
139.3D6.2A$473.A147.D2.2D$473.A.A7.D$474.2A6.3D75.2A$481.2D2.D74.A$
558.A.A25.2A3.2A$500.A9.A15.A31.2A26.2A3.2A$500.3A5.3A13.3A$503.A3.A
15.A27.2D2.D$502.2A3.2A14.2A27.3D24.2A$553.D4.2A20.A$558.2A20.A.A$
581.2A$538.D$515.D21.D78.D$515.3D18.2D78.2D9.A$515.D.D15.2A2.2D78.2D
7.A.A$490.D26.D15.2A3.D78.D8.A.A$479.A9.2D62.2A61.D10.A$478.A.A7.2D
62.A2.A3.2A23.2A$478.A.A8.D63.2A4.2A24.A$479.A10.D91.3A28.2A3.2A$582.
A31.A3.2A7.2A$536.2A73.3A13.2A$487.2A27.2A19.A73.A$478.2A7.2A7.A6.2A
11.A.A15.3A$478.2A14.3A6.2A13.A15.A$493.A24.2A$493.2A$597.2A$597.2A$
589.2A$590.A6.3D$587.3A8.D$587.A10.3D2$588.A$587.A.A$587.A.A$585.3A.
2A$584.A$585.3A.2A$587.A.2A2$597.2A$597.2A7.2A$606.A$604.A.A$604.2A4$
584.2A$584.2A2$99.A$97.3A$96.A26.A$96.2A25.3A474.A$126.A472.A.A$125.
2A472.A.A$600.A$56.A49.A494.3A$40.A15.3A47.3A40.2A452.A$38.3A18.A49.A
39.A$37.A20.2A11.2A11.D23.2A11.2A11.D12.A.A$37.2A32.2A9.3D36.2A9.3D
12.2A4.2A$82.D.D47.D.D18.A$82.D49.D18.A.A$14.2A4.2A129.2A$14.2A3.A2.A
$20.2A$36.D3.2A15.D49.D$36.2D2.2A15.D.D47.D.D41.2A$37.2D18.3D36.2A9.
3D41.A.A$37.D21.D23.2A11.2A11.D22.2A19.A$36.D47.A46.A.A19.2A$81.3A47.
A$15.2A64.A48.2A10.2A$15.2A4.D121.A$20.3D27.2A48.2A38.3A$19.D2.2D27.A
49.A38.A$48.3A20.2A25.3A20.2A$48.A22.A26.A22.A$12.2A58.3A47.3A$12.A.A
59.A49.A$14.A$14.2A148.2C$163.C2.C$154.A9.2C$153.A.A415.D$33.2A118.2A
414.D3.D$33.A540.D40.5D$31.A.A535.D4.D39.D4.D26.2A$14.2A15.2A537.5D
44.D26.2A$14.2A598.D3.D$616.D$643.2A$31.2A610.A.A$31.A.A68.A538.A.A.
3A$33.A66.3A538.2A5.A$33.2A64.A547.2A$89.2A8.2A$90.A$58.2A11.A18.A.A$
58.2A10.A.A18.2A$24.3D43.A.A32.2A57.2A$15.2A8.D43.2A.3A2.2A26.2A57.2A
$16.A6.3D49.A2.A$13.3A53.2A.3A3.A.A83.3D$13.A55.2A.A6.2A84.D$105.2A
58.3D$105.2A2$31.2A$31.A.A$33.A$33.2A31.2A11.D.2A$66.2A9.3D.2A$51.2A
24.D.D27.2A$50.A2.A23.D29.A$49.A.2A52.A.A$49.A55.2A$48.2A$23.2A38.2A$
14.2A7.2A38.A$15.A48.3A$15.A.A7.D40.A99.2A$16.2A6.3D139.2A7.2A$23.2D
2.D147.A$165.D7.A.A$87.2A75.3D6.2A$88.A74.D2.2D$56.2A3.2A25.A.A$56.2A
3.2A26.2A31.A15.A9.A$122.3A13.3A5.3A$93.D2.2D27.A15.A3.A$68.2A24.3D
27.2A14.2A3.2A$68.A20.2A4.D$66.A.A20.2A$66.2A$110.D$32.D78.D21.D$21.A
9.2D78.2D18.3D$20.A.A7.2D78.2D2.2A15.D.D$20.A.A8.D78.D3.2A15.D26.D$
21.A10.D61.2A62.2D9.A$63.2A23.2A3.A2.A62.2D7.A.A$63.A24.2A4.2A63.D8.A
.A$29.2A3.2A28.3A91.D10.A$20.2A7.2A3.A31.A$20.2A13.3A73.2A$37.A73.A
19.2A27.2A$112.3A15.A.A11.2A6.A7.2A7.2A$114.A15.A13.2A6.3A14.2A$129.
2A24.A$154.2A$50.2A$50.2A$58.2A$49.3D6.A$50.D8.3A$48.3D10.A2$60.A$59.
A.A$59.A.A$58.2A.3A$64.A$58.2A.3A$58.2A.A2$50.2A$41.2A7.2A$42.A$42.A.
A$43.2A4$63.2A$63.2A2$549.A$549.3A$525.A26.A$48.A474.3A25.2A$47.A.A
472.A$47.A.A472.2A$48.A$45.3A494.A49.A$45.A452.2A40.3A47.3A15.A$499.A
39.A49.A18.3A$499.A.A12.D11.2A11.2A23.D11.2A11.2A20.A$494.2A4.2A12.3D
9.2A36.3D9.2A32.2A$495.A18.D.D47.D.D$495.A.A18.D49.D$496.2A129.2A4.2A
$626.A2.A3.2A$627.2A$541.D49.D15.2A3.D$496.2A41.D.D47.D.D15.2A2.2D$
495.A.A41.3D9.2A36.3D18.2D$495.A19.2A22.D11.2A11.2A23.D21.D$494.2A19.
A.A46.A47.D$517.A47.3A$505.2A10.2A48.A64.2A$505.A121.D4.2A$506.3A38.
2A48.2A27.3D$508.A38.A49.A27.2D2.D$526.2A20.3A25.2A20.3A$527.A22.A26.
A22.A$524.3A47.3A58.2A$524.A49.A59.A.A$634.A$483.2C148.2A$482.C2.C$
483.2C9.A$77.D415.A.A$75.D3.D414.2A118.2A$29.5D40.D540.A$.2A26.D4.D
39.D4.D535.A.A$.2A26.D44.5D537.2A15.2A$30.D3.D598.2A$32.D$4.2A$3.A.A
610.2A$.3A.A.A538.A68.A.A$A5.2A538.3A66.A$2A547.A64.2A$548.2A8.2A$
558.A$556.A.A18.A11.2A$556.2A18.A.A10.2A$483.2A57.2A32.A.A43.3D$483.
2A57.2A26.2A2.3A.2A43.D8.2A$570.A2.A49.3D6.A$482.3D83.A.A3.3A.2A53.3A
$483.D84.2A6.A.2A55.A$481.3D58.2A$542.2A2$616.2A$615.A.A$615.A$566.2A
.D11.2A31.2A$566.2A.3D9.2A$540.2A27.D.D24.2A$541.A29.D23.A2.A$541.A.A
52.2A.A$542.2A55.A$599.2A$584.2A38.2A$585.A38.2A7.2A$582.3A48.A$481.
2A99.A40.D7.A.A$472.2A7.2A139.3D6.2A$473.A147.D2.2D$473.A.A7.D$474.2A
6.3D75.2A$481.2D2.D74.A$558.A.A25.2A3.2A$500.A9.A15.A31.2A26.2A3.2A$
500.3A5.3A13.3A$503.A3.A15.A27.2D2.D$502.2A3.2A14.2A27.3D24.2A$553.D
4.2A20.A$558.2A20.A.A$581.2A$538.D$515.D21.D78.D$515.3D18.2D78.2D9.A$
515.D.D15.2A2.2D78.2D7.A.A$490.D26.D15.2A3.D78.D8.A.A$479.A9.2D62.2A
61.D10.A$478.A.A7.2D62.A2.A3.2A23.2A$478.A.A8.D63.2A4.2A24.A$479.A10.
D91.3A28.2A3.2A$582.A31.A3.2A7.2A$536.2A73.3A13.2A$487.2A27.2A19.A73.
A$478.2A7.2A7.A6.2A11.A.A15.3A$478.2A14.3A6.2A13.A15.A$493.A24.2A$
493.2A$597.2A$597.2A$589.2A$590.A6.3D$587.3A8.D$587.A10.3D2$588.A$
587.A.A$587.A.A$585.3A.2A$584.A$585.3A.2A$587.A.2A2$597.2A$597.2A7.2A
$606.A$604.A.A$604.2A4$584.2A$584.2A5$600.A$599.A.A$599.A.A$600.A$
601.3A$603.A27$571.A$569.A3.A$574.A40.5A$569.A4.A39.A4.A26.2A$570.5A
44.A26.2A$614.A3.A$616.A$643.2A$643.A.A$641.A.A.3A$641.2A5.A$647.2A!
#C [[ STEP 20 ]]

Population is 496 cells, there are only two eater2s, repeat time is 90 ticks, vertical offset is 128 cells (or anything between 101-131 cells really) and travel time from input to output is 0 mod 4, just to keep Hashlife happy. I think this one might well turn out to be worth programming...!

Again I ended up doing the search manually, using the H-to-H and H-to-G collections. Once the H-to-Gs have been catalogued properly -- Spartan vs. non-Spartan, and the repeat time for each -- it will be possible to write a script to maybe find something with a slightly smaller population, and/or a construction-arm lane with more clearance.

Or maybe someone can find an improvement even without an automated search. I started investigating this geometry only this evening, and really tried just a few obvious Herschel conduits and H-to-Gs before something worked. The diagonal adjustment for the two circuits allows for half a dozen ways to shoot down the beehive, either just before or just after the paired signal gets there to make the MWSS. For example, it actually works just as well to move the MWSS-making circuit two cells SE (in the first, SE-most copy of the circuit).

----------------------------------------------

So... 495 ON cells or less, anyone? -- keeping the 128-cell offset, 90-tick repeat time, and 0-mod-4 timing, and not adding too many more expensive still lifes. Though I suppose if a Snark could really cut down on the size, it would be worth trying out the new slow-salvo Snark recipes.

The xs14_354cgs26 has some clearance, but it's still dangerously close to the construction arm. I haven't checked those recipes yet, so am just keeping my fingers crossed there will be a good way to build that still life.

Another limitation of the Orthogonoid494 design is that there are no easily liberated gliders heading SE. That just means that self-destruct still lifes should be added, so that old empty circuits to the south can be shot down with a single LWSS, or maybe a single glider following a chain of one-time turners.

Or the destruction reaction could be triggered by an LWSS following the MWSS recipe stream, and could produce a 180-degree output LWSS in exactly the right spacetime location, analogous to the cleanup glider in the Demonoid.

Either of those is probably easier to deal with than blocking up the construction arm and unblocking a new destruction arm, anyway -- though that did seem like an interesting idea...!
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Re: Orthogonoid working notes

Postby dvgrn » November 13th, 2016, 10:32 am

dvgrn wrote:The xs14_354cgs26 has some clearance, but it's still dangerously close to the construction arm. I haven't checked those recipes yet, so am just keeping my fingers crossed there will be a good way to build that still life.

Extrementhusiast and chris_c posted some possible seeds for eater on eater -- looks like the one in that link can be made to work:

x = 18, y = 23, rule = LifeHistory
10.2A$2.A7.2A$A.A$.2A2$8.2A$8.A.A$9.A$4.2A$3.A.A$4.A4.A$8.A.A5.2A$8.A
.CD4.2A$9.AD.D$8.D.D.3D$8.2D5.D$14.2D5$6.2A$6.2A!

Not sure if there might be a way to set up the following reaction instead. I suppose the cost would probably end up about the same:

x = 15, y = 14, rule = LifeHistory
9.2A$9.2A3$8.A$5.A2.A$6.3A2$3.2D$3.D.D$.D.D.3D4.2A$.2D5.D2.A2.A$2A5.
2D3.2A$2A!

EDIT: One way to build the xs14_354cgs26 eater-on-eater would be to use chris_c's trick from the Demonoid, sending 180-degree gliders back from the elbow -- assuming that single-channel recipes can be found for a wide enough range of lanes (I kind of forget if that has already been figured out). But I don't really want to do that, for the following reason:

The simplest and most efficient Orthogonoid will basically just look like a long horizontal line, with the construction data folded over between the two replicator units at the ends -- very much analogous to the equally boring diagonal-line Demonoid. But what I really want is a rectangular model, like this:

Orthogonoid-diagram.png
rough diagram of rectangular Orthogonoid spaceship
Orthogonoid-diagram.png (15.14 KiB) Viewed 10293 times

The job of the first line of MWSSes is to tell the lead construction arm (on the right side, halfway down the diagram) to start with an elbow at (Ex, Ey) and a target object at (Tx, Ty), and make
1) an identical new target object at (Tx, Ty-128);
2) an identical new elbow at (Ex, Ey-128).
Not sure exactly how to get that new elbow in place, but with any luck the timing will work out so that a glider can be bounced back from near (Tx, Ty-128), to be met by another glider coming from the current elbow location, which will have moved to around (Ex+64, Ey-64). That's just a detail, though -- could perfectly well use a recipe to split some junk off the elbow, and push the junk up to (Ex, Ey-128) instead.

Anyway, after the new target object and elbow are in position, the lead construction arm can back off and start working on the previous target left behind around (Tx, Ty) -- because it won't be the lead construction arm any more. The first line of MWSSes will have reflected off the opposing replicator unit and will start to activate the next constructor arm, which will immediately start working on moving target and elbow to (Tx, Ty-256) and (Ex, Ey-256).

There are a lot of signal crossings along the left and right sides where collisions are possible. But it should be no worse than the original Gemini -- I think. Just a matter of calculating the "safe zone" for placing each new pair of single-channel gliders.

Anyone see serious design flaws here, or will this thing actually fly?
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Re: Orthogonoid working notes

Postby dvgrn » November 14th, 2016, 3:18 pm

If we decided not to worry about Hashlife compatibility, there are some more options I didn't see on the last pass. Somehow I forgot about the H-to-MWSS converter's failure to produce a dependent glider, which makes a Spartan R64 usable with a compression rate better than 90 ticks after all. (Ordinarily it's 153 ticks, or else you need a very non-Spartan 7x9 eater on the inside corner).

That means there are options like Orthogonoid421, which can be adjusted down to 78 cells between replicator units:

x = 223, y = 156, rule = LifeHistory
15$75.A$73.3A38.A9.A36.A$72.A11.A29.3A5.3A27.A7.A.A$63.4B5.2A8.3A15.A
16.A3.A30.3A4.2BAB$63.11B7.A18.3A13.2A.B.2A32.A4.2B9.2A$61.11B5.B3.2A
20.A12.7B31.2A5.6B2.BA.AB$60.2A11B2.8B19.2A14.3B13.3B5.B.7B3.3B3.10B
2A2B$60.2A19B21.B13.6B11.4B.13B5.3B2.11B.B2A$61.20B19.3B9.2B2.6B4.26B
D10BD5B4.BA.A$62.20B16.6B7.4B.7B2.4BD21BD10B2D6B6.A$63.21B11.10B2.16B
2.4B3D18B2D11B2D5B.B4.2A$62.25B2.2B3.30B.4BDBD15B2A2B2D13BD4B2A$61.4B
4.14BD15B2A3BD26BD15B2A3BD12B3D2B.2A$60.4B6.6B.4BDBD15B2A2B2D30B2.2B
3.22BD2B2D3B$59.4B5.5B.B2.4B3D18B2D28B11.10B2.B3.B.2B.6B$58.4B6.2A7.
4BD21BD26B16.6B11.7B$57.4B8.A8.26BD24B19.3B13.6B$57.3B6.3A16.4B.13B3.
B.22B20.B9.B.9B$57.2B7.A19.3B5.B.7B7.11B2.7B20.2A6.2A12B$87.4B20.3B.
4B6.3B.B2A19.A6.2A12B$89.2A19.A4.2B2AB9.BA.A15.3A7.14B$89.A18.3A6.2A
13.A15.A9.12B.B2A$90.3A14.A24.2A22.2AB.9B2.BA.A$92.A14.2A46.A.AB.8B6.
A$84.A70.A5.8B5.2A$84.3A67.2A6.7B$87.A71.11B$86.2A8.2A60.12B$86.5B5.A
61.12B$88.4B.BA.A18.A11.2A29.11B$81.B4.6B.B2A18.A.A9.B2AB28.B3D4B.4B$
80.2AB.10B20.A.A9.3B29.2BD4B4.2A$80.2A12B14.2A2.3A.2A9.B.B28.2B3D2B4.
A$45.B35.B.11B14.A2.A4.B8.5B28.6B6.3A$43.4B36.13B3.4B2.BA.A3.3AB2A6.
6B27.7B8.A$42.6B33.2B.12B2.5B2.B2A6.A.2A4.8B26.8B$41.10B.3B25.2A24B
10.13B26.8B$40.16B24.2A24B12.13B24.8B$39.15BA2B24.B.B.20B12.15B21.2AB
2.6B$15.B.B.B.B.B.B.B.B.B.B.B.16BABA28.20B2.B10.15B20.A.AB.7B$15.39B
2A27.26B5.B.17B19.A4.6B$15.40B27.51B18.2A4.6B$15.38B30.21B2ABD11B2A
13B23.6B$15.39B29.21B2AB3D9B2A14B21.8B$15.39B24.2A4.23BDBD20B3.B2A21.
8B$16.B.B.B.B.B.B.B.B.B.B.B.16B25.A4.25BD19B4.A2.A19.9B$40.14B25.A.AB
.29B2.2B2.B3.6B5.2A.A18.9B$40.13B27.2AB.13B.7B2.4B13.6B7.A18.10B$40.
11B31.15B2.6B17.9B6.2A17.5B2A3B$39.13B30.4B.10B3.3B19.2A4.4B24.5B2A4B
3.2A$38.15B30.14B4.B21.A5.4B23.11B3.A$37.16B31.12B24.3A7.4B22.4BD7BA.
A$36.17B32.11B24.A10.4B23.B3D4B2.2A$37.16B32.11B36.4B22.D2B2D2B$38.
13B35.9B63.5B$38.5B2A2B39.9B63.5B$40.3B2A2B39.9B3.2A35.4B18.7B$40.8B
38.9B3.A24.2A3.2A6.4B18.6B$39.8B40.9BA.A23.B2AB.B2AB6.4B17.5B$39.8B
17.A23.6B2.2A25.2B2.3B3.B4.4B13.8B$39.7B16.3A19.10B30.3B.3B.4B3.4B10.
10B$39.7B15.A21.6B2D2BD22.2A5.7B.13B8.12B$40.6B15.2A20.7B3DB.2B20.A5.
23B6.13B$40.6B13.4B19.9BD4B2A19.A.AB.19B.8B2.12B$41.5B12.3B5.B.7B7.
14B2A20.2AB.29B.13B$41.6B10.4B.13B4.B2.13B.B23.45B$40.6B4.26BD18B25.
33BD13B$40.7B2.4BD21BD18B26.33B2D9BA4B$41.6B2.4B3D18B2D18B27.33B2D7BA
BA4B$41.7B.4BDBD15B2A2B2D17B29.31BD8BABA4B$40.15BD15B2A3BD18B26.32BD
10BA4B$40.19B2.2B3.11B2.2B3.7B2A2B.2B23.2A3.25B4.4B3.5B$39.17B11.10B
8.B.3BA2BA3B2A23.A3.20B4.B3.3B7.B$35.B3.15B16.6B13.2B2A2B.B2A20.3A6.
15B7.2A2.B2AB5.3B$34.2AB.15B19.3B14.6B2.B21.A8.11B12.A3.2A6.B2AB$34.
2A18B20.B15.4B33.13B8.3A13.2A$35.B.3B2A12B20.2A14.4B32.15B7.A$38.2B2A
11B22.A15.2B33.16B$39.2B2.10B19.3A51.17B$38.2B3.6B.B21.A53.16B$37.B2A
B2.4B81.13B$38.2A3.2B2AB80.3B.2B2A5B$45.2A79.4B2.2B2A3B$126.2A3.8B$
127.A4.2B3D3B$124.3A5.3BD4B$124.A8.2B3D2B$133.7B$125.A7.6B$124.A.A6.
6B$124.A.A6.5B$122.3A.2A4.6B$121.A4.B6.6B$122.3AB2AB3.7B$124.A.2AB.8B
$128.10B$128.6B2A3B$128.6B2A2B5.2A$128.10B5.A$127.11B2.BA.A$127.12B.B
2A$126.15B$125.16B$122.2B.16B$121.2A18B$121.2AB.17B$122.B.4B.8B2.4B$
129.7B4.4B$130.6B5.4B$132.4B6.4B$134.3BA5.4B$135.BA.A5.4B$136.A.A6.4B
$137.A8.4B$138.3A6.4B$140.A7.4B$149.4B$67.B.B.B.B.B.B.B.B.C.B.B.B.B.B
.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.5B$67.14BC3BC
70B$67.19BC40B5C25B.B$67.14BC4BC39BC4BC26B2A$67.15B5C44BC26B2A$67.59B
C3BC25B2.B$68.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B
.B.B.C.B.B.B.B.B.B.B.B.B.B.B.B2.2B$154.B2A$155.A.A$153.A.A.3A$153.2A
5.A$159.2A!
[[ STEP 20 ]]

Or here's Orthogonoid412 -- it has an 86-cell offset and a lower population, but would probably work best as a straight-line Orthogonoid, not a rectangular model, because of the signal crossings near the eater-on-eater:

x = 395, y = 427, rule = LifeHistory
38.4B$39.4B$40.4B$41.4B$42.4B$43.4B$44.4B$45.4B$46.4B$47.4B$48.4B$49.
4B$50.4B$51.4B$52.4B$53.4B$54.4B$55.4B$56.4B$57.4B26.A$58.4B23.3A$59.
4B21.A$60.4B20.2A$61.4B17.4B$62.4B15.3B26.AB$63.4B14.4B24.A.AB.B$44.A
19.4B12.5B8.2A13.B.2A2B2A$28.A15.3A12.B.3B.4B11.6B8.A11.6B.B2A$26.3A
18.A10.18B2.8B8.A.AB7.6B3.B$8.2B15.A20.2A3.B5.2B2A11BD14B8.2AB.3B3.7B
$7.4B14.2A19.8B3.2B2A9B3D13B11.16B$7.4B15.B21.8B.13BDBD4B.7B12.16B$3.
B2.6B14.3B19.22BD15B12.15B$2.2AB.2B2A2B13.6B16.15B.2B2.19B11.16B$2.2A
3BA2BA3B.B8.10B10.18B8.17B8.18B$3.2B.2B2A7B3.2B2.11B3.2B2.19B11.15B.
2B2.20B$6.18BD3B2A15BD15B12.22BD16B$7.17B2D2B2A15BDBD4B.7B13.8B.13BDB
D4B.9B$7.18B2D18B3D13B10.8B3.2B2A9B3D4B2.7B$7.18BD21BD14B9.2A3.B5.2B
2A11BD4B2.7B$6.18BD26B2.8B11.A10.18B4.6B$4.B.13B2.B4.13B.4B2.3B6.6B8.
3A12.B.3B.4B10.7B$3.2AB.12B7.7B.B5.3B5.B6.5B9.A20.3B12.6B$3.2A4BD9B
19.4B14.4B28.4B13.7B$4.2B.B3D7B20.2A16.3B29.2A16.5B$7.D2B2D6B21.A17.
4B28.A16.6B$7.10B19.3A20.2A25.3A15.9B$6.7B23.A22.A26.A17.2A.7B$2A5.7B
46.3A42.A5.4B$A.A3.8B48.A39.3A7.4B$2.A3.8B88.A10.4B$2.2A.9B100.4B$4.
11B100.4B$4.12B100.4B$4.12B101.4B$5.10B6.2A95.4B$3.11B7.A75.A21.4B$3.
14B.BA.A73.3A22.4B$2.2A13B.B2A73.A26.4B$2.2A15B65.2A8.2A26.4B$3.B.15B
65.A5.5B27.4B$5.14B34.2A11.A18.A.AB.4B30.4B$6.11B.B2A31.B2AB9.A.A18.
2AB.6B4.B24.4B$6.9B3.BA.A31.3B9.A.A20.10B.B2A24.4B$5.8B8.A30.B.B9.2A.
3A2.2A14.12B2A25.4B$5.7B9.2A29.5B8.B4.A2.A14.11B.B27.4B4.B$4.11B37.6B
6.2AB3A3.A.AB2.4B3.13B30.4B2.4B$4.12B36.8B4.2A.A6.2AB2.5B2.12B.2B29.
10B$4.12B37.13B10.24B2A25.3B.10B$5.11B35.13B12.24B2A24.16B$3.4B.4B3DB
34.15B12.20B.B.B24.2BA15B$3.2A4.4BD2B34.15B10.B2.20B28.ABA16B.B.B.B.B
$4.A4.2B3D2B33.17B.B5.26B27.2A26B$.3A6.6B33.51B27.27B$.A8.7B31.13B2A
11BDB2A21B30.25B$10.8B29.14B2A9B3DB2A21B29.26B$11.8B27.2AB3.20BDBD23B
4.2A24.26B$11.8B26.A2.A4.19BD25B4.A25.16B.B.B.B.B.B$10.6B2.B2A23.A.2A
5.6B3.B2.2B2.29B.BA.A25.14B$10.7B.BA.A22.A7.6B13.4B2.7B.13B.B2A27.13B
$11.6B4.A21.2A6.9B17.6B2.15B31.11B$11.6B4.2A27.4B4.2A19.3B3.10B.4B30.
13B$11.6B32.4B5.A21.B4.14B30.15B$10.8B30.4B7.3A24.12B31.16B$9.8B30.4B
10.A24.11B32.17B$9.9B28.4B36.11B32.16B$9.9B27.4B38.9B35.13B209.4B$8.
10B26.4B39.9B39.2B2A5B208.4B$8.3B2A5B25.4B35.2A3.9B39.2B2A3B209.4B$2.
2A3.4B2A5B24.4B37.A3.9B38.8B208.4B$3.A3.11B23.4B38.A.A9B40.8B206.4B$
3.A.A7BD4B22.4B40.2A2.6B23.A17.8B205.4B$4.2A2.4B3DB23.4B45.10B19.3A
16.7B204.4B$9.2B2D2BD22.4B46.D2B2D6B21.A15.7B203.4B$11.5B21.4B44.2B.B
3D7B20.2A15.6B203.4B$11.5B20.4B44.2A4BD9B19.4B13.6B202.4B$10.7B18.4B
45.2A14B7.7B.B5.3B12.5B202.4B$10.6B18.4B6.2A3.2A34.B.13B2.B4.13B.4B
10.6B201.4B$11.5B17.4B6.B2AB.B2AB35.18BD26B4.6B199.4B$11.8B13.4B4.B3.
3B2.2B37.18BD21BD4B2.7B198.4B$11.10B10.4B3.4B.3B.3B38.18B2D18B3D4B2.
6B198.4B$10.12B8.13B.7B5.2A30.17B2D2B2A15BDBD4B.7B197.4B$9.13B6.23B5.
A30.18BD3B2A15BD15B195.4B$10.12B2.8B.19B.BA.A27.2B.2B2A7B3.2B2.11B3.
2B2.19B194.4B$9.13B.29B.B2A27.2A3BA2BA3B.B8.10B11.17B192.4B$9.45B29.
2AB.2B2A2B13.6B16.15B3.B160.A26.4B$7.13BD33B30.B2.6B14.3B19.15B.B2A
159.3A23.4B$5.4BA9B2D33B34.4B15.B20.18B2A162.A21.4B$4.4BABA7B2D33B35.
4B14.2A20.12B2A3B.B162.2A20.4B$4.4BABA8BD31B38.2B15.A22.11B2A2B165.4B
17.4B$5.4BA10BD32B54.3A19.10B2.2B140.BA26.3B15.4B$7.5B3.4B4.25B3.2A
56.A21.B.6B3.2B136.B.BA.A24.4B14.4B$9.B7.3B3.B4.20B3.A83.4B2.B2AB134.
2A2B2A.B13.2A8.5B12.4B19.A$8.3B5.B2AB2.2A7.15B6.3A79.B2A2B3.2A135.2AB
.6B11.A8.6B11.4B.3B.B12.3A15.A$7.B2AB6.2A3.A12.11B8.A80.2A143.B3.6B7.
BA.A8.8B2.18B10.A18.3A$8.2A13.3A8.13B236.7B3.3B.B2A8.14BD11B2A2B5.B3.
2A20.A15.2B$25.A7.15B234.16B11.13B3D9B2A2B3.8B19.2A14.4B$32.16B234.
16B12.7B.4BDBD13B.8B21.B15.4B$31.17B234.15B12.15BD22B19.3B14.6B2.B$
32.16B234.16B11.19B2.2B.15B16.6B13.2B2A2B.B2A$33.13B236.18B8.17B8.18B
10.10B8.B.3BA2BA3B2A$33.5B2A2B.3B237.20B2.2B.15B11.19B2.2B3.11B2.2B3.
7B2A2B.2B$35.3B2A2B2.4B235.16BD22B12.15BD15B2A3BD18B$35.8B3.2A235.9B.
4BDBD13B.8B13.7B.4BDBD15B2A2B2D17B$34.3B3D2B4.A237.7B2.4B3D9B2A2B3.8B
10.13B3D18B2D18B$34.4BD3B5.3A234.7B2.4BD11B2A2B5.B3.2A9.14BD21BD18B$
34.2B3D2B8.A234.6B4.18B10.A11.8B2.26BD18B$34.7B243.7B10.4B.3B.B12.3A
8.6B6.3B2.4B.13B4.B2.13B.B$35.6B7.A4B231.6B12.3B20.A9.5B6.B5.3B5.B.7B
7.12B.B2A$35.6B6.ABA2B231.7B13.4B28.4B14.4B19.9BD4B2A$36.5B6.ABAB233.
5B16.2A29.3B16.2A20.7B3DB.2B$36.6B4.2AB3A231.6B16.A28.4B17.A21.6B2D2B
D$35.6B6.B4.A229.9B15.3A25.2A20.3A19.10B$35.7B3.B2AB3A229.7B.2A17.A
26.A22.A23.7B$36.8B.B2A.A230.4B5.A42.3A46.7B5.2A$36.10B233.4B7.3A39.A
48.8B3.A.A$35.3B2A6B232.4B10.A88.8B3.A$29.2A5.2B2A6B231.4B100.9B.2A$
30.A5.10B230.4B100.11B$30.A.AB2.11B228.4B100.12B$31.2AB.12B227.4B101.
12B$33.15B225.4B95.2A6.10B$33.16B223.4B21.A75.A7.11B$33.16B.2B219.4B
22.3A73.A.AB.14B$33.18B2A217.4B26.A73.2AB.13B2A$32.17B.B2A216.4B26.2A
8.2A65.15B2A$31.4B2.8B.4B.B216.4B27.5B5.A65.15B.B$30.4B4.7B222.4B30.
4B.BA.A18.A11.2A34.14B$29.4B5.6B222.4B24.B4.6B.B2A18.A.A9.B2AB31.2AB.
11B$28.4B6.4B223.4B24.2AB.10B20.A.A9.3B31.A.AB3.9B$27.4B5.A3B224.4B
25.2A12B14.2A2.3A.2A9.B.B30.A8.8B$26.4B5.A.AB219.B4.4B27.B.11B14.A2.A
4.B8.5B29.2A9.7B$25.4B6.A.A218.4B2.4B30.13B3.4B2.BA.A3.3AB2A6.6B37.
11B$24.4B8.A218.10B29.2B.12B2.5B2.B2A6.A.2A4.8B36.12B$23.4B6.3A218.
10B.3B25.2A24B10.13B37.12B$22.4B7.A219.16B24.2A24B12.13B35.11B$21.4B
227.15BA2B24.B.B.20B12.15B34.B3D4B.4B$20.5B.B.B.B.B.B.B.B.B.B.B.B.B.B
.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.D.B.B.B.B.B.B.B.B.B.B.B129.B.B
.B.B.16BABA28.20B2.B10.15B34.2BD4B4.2A$18.70BD3BD20B128.26B2A27.26B5.
B.17B33.2B3D2B4.A$15.B.25B5D40BD25B128.27B27.51B33.6B6.3A$14.2A26BD4B
D39BD4BD20B128.25B30.21B2ABD11B2A13B31.7B8.A$14.2A26BD44B5D21B128.26B
29.21B2AB3D9B2A14B29.8B$15.B2.25BD3BD65B128.26B24.2A4.23BDBD20B3.B2A
27.8B$17.2B2.B.B.B.B.B.B.B.B.B.B.B.B.D.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.
B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B129.B.B.B.B.B.16B25.A4.25BD19B4.A
2.A26.8B$17.2AB233.14B25.A.AB.29B2.2B2.B3.6B5.2A.A23.2AB2.6B$16.A.A
234.13B27.2AB.13B.7B2.4B13.6B7.A22.A.AB.7B$14.3A.A.A232.11B31.15B2.6B
17.9B6.2A21.A4.6B$13.A5.2A231.13B30.4B.10B3.3B19.2A4.4B27.2A4.6B$13.
2A236.15B30.14B4.B21.A5.4B32.6B$250.16B31.12B24.3A7.4B30.8B$249.17B
32.11B24.A10.4B30.8B$250.16B32.11B36.4B28.9B$38.4B209.13B35.9B38.4B
27.9B$39.4B208.5B2A2B39.9B39.4B26.10B$40.4B209.3B2A2B39.9B3.2A35.4B
25.5B2A3B$41.4B208.8B38.9B3.A37.4B24.5B2A4B3.2A$42.4B206.8B40.9BA.A
38.4B23.11B3.A$43.4B205.8B17.A23.6B2.2A40.4B22.4BD7BA.A$44.4B204.7B
16.3A19.10B45.4B23.B3D4B2.2A$45.4B203.7B15.A21.6B2D2BD46.4B22.D2B2D2B
$46.4B203.6B15.2A20.7B3DB.2B44.4B21.5B$47.4B202.6B13.4B19.9BD4B2A44.
4B20.5B$48.4B202.5B12.3B5.B.7B7.14B2A45.4B18.7B$49.4B201.6B10.4B.13B
4.B2.13B.B34.2A3.2A6.4B18.6B$50.4B199.6B4.26BD18B35.B2AB.B2AB6.4B17.
5B$51.4B198.7B2.4BD21BD18B37.2B2.3B3.B4.4B13.8B$52.4B198.6B2.4B3D18B
2D18B38.3B.3B.4B3.4B10.10B$53.4B197.7B.4BDBD15B2A2B2D17B30.2A5.7B.13B
8.12B$54.4B195.15BD15B2A3BD18B30.A5.23B6.13B$55.4B194.19B2.2B3.11B2.
2B3.7B2A2B.2B27.A.AB.19B.8B2.12B$56.4B192.17B11.10B8.B.3BA2BA3B2A27.
2AB.29B.13B$57.4B26.A160.B3.15B16.6B13.2B2A2B.B2A29.45B$58.4B23.3A
159.2AB.15B19.3B14.6B2.B30.33BD13B$59.4B21.A162.2A18B20.B15.4B34.33B
2D9BA4B$60.4B20.2A162.B.3B2A12B20.2A14.4B35.33B2D7BABA4B$61.4B17.4B
165.2B2A11B22.A15.2B38.31BD8BABA4B$62.4B15.3B26.AB140.2B2.10B19.3A54.
32BD10BA4B$63.4B14.4B24.A.AB.B136.2B3.6B.B21.A56.2A3.25B4.4B3.5B$44.A
19.4B12.5B8.2A13.B.2A2B2A134.B2AB2.4B83.A3.20B4.B3.3B7.B$28.A15.3A12.
B.3B.4B11.6B8.A11.6B.B2A135.2A3.2B2AB79.3A6.15B7.2A2.B2AB5.3B$26.3A
18.A10.18B2.8B8.A.AB7.6B3.B143.2A80.A8.11B12.A3.2A6.B2AB$8.2B15.A20.
2A3.B5.2B2A11BD14B8.2AB.3B3.7B236.13B8.3A13.2A$7.4B14.2A19.8B3.2B2A9B
3D13B11.16B234.15B7.A$7.4B15.B21.8B.13BDBD4B.7B12.16B234.16B$3.B2.6B
14.3B19.22BD15B12.15B234.17B$2.2AB.2B2A2B13.6B16.15B.2B2.19B11.16B
234.16B$2.2A3BA2BA3B.B8.10B10.18B8.17B8.18B236.13B$3.2B.2B2A7B3.2B2.
11B3.2B2.19B11.15B.2B2.20B237.3B.2B2A5B$6.18BD3B2A15BD15B12.22BD16B
235.4B2.2B2A3B$7.17B2D2B2A15BDBD4B.7B13.8B.13BDBD4B.9B235.2A3.8B$7.
18B2D18B3D13B10.8B3.2B2A9B3D4B2.7B237.A4.2B3D3B$7.18BD21BD14B9.2A3.B
5.2B2A11BD4B2.7B234.3A5.3BD4B$6.18BD26B2.8B11.A10.18B4.6B234.A8.2B3D
2B$4.B.13B2.B4.13B.4B2.3B6.6B8.3A12.B.3B.4B10.7B243.7B$3.2AB.12B7.7B.
B5.3B5.B6.5B9.A20.3B12.6B231.4BA7.6B$3.2A4BD9B19.4B14.4B28.4B13.7B
231.2BABA6.6B$4.2B.B3D7B20.2A16.3B29.2A16.5B233.BABA6.5B$7.D2B2D6B21.
A17.4B28.A16.6B231.3AB2A4.6B$7.10B19.3A20.2A25.3A15.9B229.A4.B6.6B$6.
7B23.A22.A26.A17.2A.7B229.3AB2AB3.7B$2A5.7B46.3A42.A5.4B230.A.2AB.8B$
A.A3.8B48.A39.3A7.4B233.10B$2.A3.8B88.A10.4B232.6B2A3B$2.2A.9B100.4B
231.6B2A2B5.2A$4.11B100.4B230.10B5.A$4.12B100.4B228.11B2.BA.A$4.12B
101.4B227.12B.B2A$5.10B6.2A95.4B225.15B$3.11B7.A75.A21.4B223.16B$3.
14B.BA.A73.3A22.4B219.2B.16B$2.2A13B.B2A73.A26.4B217.2A18B$2.2A15B65.
2A8.2A26.4B216.2AB.17B$3.B.15B65.A5.5B27.4B216.B.4B.8B2.4B$5.14B34.2A
11.A18.A.AB.4B30.4B222.7B4.4B$6.11B.B2A31.B2AB9.A.A18.2AB.6B4.B24.4B
222.6B5.4B$6.9B3.BA.A31.3B9.A.A20.10B.B2A24.4B223.4B6.4B$5.8B8.A30.B.
B9.2A.3A2.2A14.12B2A25.4B224.3BA5.4B$5.7B9.2A29.5B8.B4.A2.A14.11B.B
27.4B4.B219.BA.A5.4B$4.11B37.6B6.2AB3A3.A.AB2.4B3.13B30.4B2.4B218.A.A
6.4B$4.12B36.8B4.2A.A6.2AB2.5B2.12B.2B29.10B218.A8.4B$4.12B37.13B10.
24B2A25.3B.10B218.3A6.4B$5.11B35.13B12.24B2A24.16B219.A7.4B$3.4B.4B3D
B34.15B12.20B.B.B24.2BA15B227.4B$3.2A4.4BD2B34.15B10.B2.20B28.ABA16B.
B.B.B.B129.B.B.B.B.B.B.B.B.B.B.B.D.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.
B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.5B$4.A4.2B3D2B33.17B.B5.26B27.2A26B128.
20BD3BD70B$.3A6.6B33.51B27.27B128.25BD40B5D25B.B$.A8.7B31.13B2A11BDB
2A21B30.25B128.20BD4BD39BD4BD26B2A$10.8B29.14B2A9B3DB2A21B29.26B128.
21B5D44BD26B2A$11.8B27.2AB3.20BDBD23B4.2A24.26B128.65BD3BD25B2.B$11.
8B26.A2.A4.19BD25B4.A25.16B.B.B.B.B.B129.B.B.B.B.B.B.B.B.B.B.B.B.B.B.
B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.D.B.B.B.B.B.B.B.B.B.B.B.B2.2B$
10.6B2.B2A23.A.2A5.6B3.B2.2B2.29B.BA.A25.14B233.B2A$10.7B.BA.A22.A7.
6B13.4B2.7B.13B.B2A27.13B234.A.A$11.6B4.A21.2A6.9B17.6B2.15B31.11B
232.A.A.3A$11.6B4.2A27.4B4.2A19.3B3.10B.4B30.13B231.2A5.A$11.6B32.4B
5.A21.B4.14B30.15B236.2A$10.8B30.4B7.3A24.12B31.16B$9.8B30.4B10.A24.
11B32.17B$9.9B28.4B36.11B32.16B$9.9B27.4B38.9B35.13B209.4B$8.10B26.4B
39.9B39.2B2A5B208.4B$8.3B2A5B25.4B35.2A3.9B39.2B2A3B209.4B$2.2A3.4B2A
5B24.4B37.A3.9B38.8B208.4B$3.A3.11B23.4B38.A.A9B40.8B206.4B$3.A.A7BD
4B22.4B40.2A2.6B23.A17.8B205.4B$4.2A2.4B3DB23.4B45.10B19.3A16.7B204.
4B$9.2B2D2BD22.4B46.D2B2D6B21.A15.7B203.4B$11.5B21.4B44.2B.B3D7B20.2A
15.6B203.4B$11.5B20.4B44.2A4BD9B19.4B13.6B202.4B$10.7B18.4B45.2A14B7.
7B.B5.3B12.5B202.4B$10.6B18.4B6.2A3.2A34.B.13B2.B4.13B.4B10.6B201.4B$
11.5B17.4B6.B2AB.B2AB35.18BD26B4.6B199.4B$11.8B13.4B4.B3.3B2.2B37.18B
D21BD4B2.7B198.4B$11.10B10.4B3.4B.3B.3B38.18B2D18B3D4B2.6B198.4B$10.
12B8.13B.7B5.2A30.17B2D2B2A15BDBD4B.7B197.4B$9.13B6.23B5.A30.18BD3B2A
15BD15B195.4B$10.12B2.8B.19B.BA.A27.2B.2B2A7B3.2B2.11B3.2B2.19B194.4B
$9.13B.29B.B2A27.2A3BA2BA3B.B8.10B11.17B192.4B$9.45B29.2AB.2B2A2B13.
6B16.15B3.B160.A26.4B$7.13BD33B30.B2.6B14.3B19.15B.B2A159.3A23.4B$5.
4BA9B2D33B34.4B15.B20.18B2A162.A21.4B$4.4BABA7B2D33B35.4B14.2A20.12B
2A3B.B162.2A20.4B$4.4BABA8BD31B38.2B15.A22.11B2A2B165.4B17.4B$5.4BA
10BD32B54.3A19.10B2.2B140.BA26.3B15.4B$7.5B3.4B4.25B3.2A56.A21.B.6B3.
2B136.B.BA.A24.4B14.4B$9.B7.3B3.B4.20B3.A83.4B2.B2AB134.2A2B2A.B13.2A
8.5B12.4B19.A$8.3B5.B2AB2.2A7.15B6.3A79.B2A2B3.2A135.2AB.6B11.A8.6B
11.4B.3B.B12.3A15.A$7.B2AB6.2A3.A12.11B8.A80.2A143.B3.6B7.BA.A8.8B2.
18B10.A18.3A$8.2A13.3A8.13B236.7B3.3B.B2A8.14BD11B2A2B5.B3.2A20.A15.
2B$25.A7.15B234.16B11.13B3D9B2A2B3.8B19.2A14.4B$32.16B234.16B12.7B.4B
DBD13B.8B21.B15.4B$31.17B234.15B12.15BD22B19.3B14.6B2.B$32.16B234.16B
11.19B2.2B.15B16.6B13.2B2A2B.B2A$33.13B236.18B8.17B8.18B10.10B8.B.3BA
2BA3B2A$33.5B2A2B.3B237.20B2.2B.15B11.19B2.2B3.11B2.2B3.7B2A2B.2B$35.
3B2A2B2.4B235.16BD22B12.15BD15B2A3BD18B$35.8B3.2A235.9B.4BDBD13B.8B
13.7B.4BDBD15B2A2B2D17B$34.3B3D2B4.A237.7B2.4B3D9B2A2B3.8B10.13B3D18B
2D18B$34.4BD3B5.3A234.7B2.4BD11B2A2B5.B3.2A9.14BD21BD18B$34.2B3D2B8.A
234.6B4.18B10.A11.8B2.26BD18B$34.7B243.7B10.4B.3B.B12.3A8.6B6.3B2.4B.
13B4.B2.13B.B$35.6B7.A4B231.6B12.3B20.A9.5B6.B5.3B5.B.7B7.12B.B2A$35.
6B6.ABA2B231.7B13.4B28.4B14.4B19.9BD4B2A$36.5B6.ABAB233.5B16.2A29.3B
16.2A20.7B3DB.2B$36.6B4.2AB3A231.6B16.A28.4B17.A21.6B2D2BD$35.6B6.B4.
A229.9B15.3A25.2A20.3A19.10B$35.7B3.B2AB3A229.7B.2A17.A26.A22.A23.7B$
36.8B.B2A.A230.4B5.A42.3A46.7B5.2A$36.10B233.4B7.3A39.A48.8B3.A.A$35.
3B2A6B232.4B10.A88.8B3.A$29.2A5.2B2A6B231.4B100.9B.2A$30.A5.10B230.4B
100.11B$30.A.AB2.11B228.4B100.12B$31.2AB.12B227.4B101.12B$33.15B225.
4B95.2A6.10B$33.16B223.4B21.A75.A7.11B$33.16B.2B219.4B22.3A73.A.AB.
14B$33.18B2A217.4B26.A73.2AB.13B2A$32.17B.B2A216.4B26.2A8.2A65.15B2A$
31.4B2.8B.4B.B216.4B27.5B5.A65.15B.B$30.4B4.7B222.4B30.4B.BA.A18.A11.
2A34.14B$29.4B5.6B222.4B24.B4.6B.B2A18.A.A9.B2AB31.2AB.11B$28.4B6.4B
223.4B24.2AB.10B20.A.A9.3B31.A.AB3.9B$27.4B5.A3B224.4B25.2A12B14.2A2.
3A.2A9.B.B30.A8.8B$26.4B5.A.AB219.B4.4B27.B.11B14.A2.A4.B8.5B29.2A9.
7B$25.4B6.A.A218.4B2.4B30.13B3.4B2.BA.A3.3AB2A6.6B37.11B$24.4B8.A218.
10B29.2B.12B2.5B2.B2A6.A.2A4.8B36.12B$23.4B6.3A218.10B.3B25.2A24B10.
13B37.12B$22.4B7.A219.16B24.2A24B12.13B35.11B$21.4B227.15BA2B24.B.B.
20B12.15B34.B3D4B.4B$20.5B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.
B.B.B.B.B.B.B.B.B.B.B.D.B.B.B.B.B.B.B.B.B.B.B129.B.B.B.B.16BABA28.20B
2.B10.15B34.2BD4B4.2A$18.70BD3BD20B128.26B2A27.26B5.B.17B33.2B3D2B4.A
$15.B.25B5D40BD25B128.27B27.51B33.6B6.3A$14.2A26BD4BD39BD4BD20B128.
25B30.21B2ABD11B2A13B31.7B8.A$14.2A26BD44B5D21B128.26B29.21B2AB3D9B2A
14B29.8B$15.B2.25BD3BD65B128.26B24.2A4.23BDBD20B3.B2A27.8B$17.2B2.B.B
.B.B.B.B.B.B.B.B.B.B.D.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.
B.B.B.B.B.B.B.B.B.B129.B.B.B.B.B.16B25.A4.25BD19B4.A2.A26.8B$17.2AB
233.14B25.A.AB.29B2.2B2.B3.6B5.2A.A23.2AB2.6B$16.A.A234.13B27.2AB.13B
.7B2.4B13.6B7.A22.A.AB.7B$14.3A.A.A232.11B31.15B2.6B17.9B6.2A21.A4.6B
$13.A5.2A231.13B30.4B.10B3.3B19.2A4.4B27.2A4.6B$13.2A236.15B30.14B4.B
21.A5.4B32.6B$250.16B31.12B24.3A7.4B30.8B$249.17B32.11B24.A10.4B30.8B
$250.16B32.11B36.4B28.9B$251.13B35.9B38.4B27.9B$251.5B2A2B39.9B39.4B
26.10B$253.3B2A2B39.9B3.2A35.4B25.5B2A3B$253.8B38.9B3.A37.4B24.5B2A4B
3.2A$252.8B40.9BA.A38.4B23.11B3.A$252.8B17.A23.6B2.2A40.4B22.4BD7BA.A
$252.7B16.3A19.10B45.4B23.B3D4B2.2A$252.7B15.A21.6B2D2BD46.4B22.D2B2D
2B$253.6B15.2A20.7B3DB.2B44.4B21.5B$253.6B13.4B19.9BD4B2A44.4B20.5B$
254.5B12.3B5.B.7B7.14B2A45.4B18.7B$254.6B10.4B.13B4.B2.13B.B34.2A3.2A
6.4B18.6B$253.6B4.26BD18B35.B2AB.B2AB6.4B17.5B$253.7B2.4BD21BD18B37.
2B2.3B3.B4.4B13.8B$254.6B2.4B3D18B2D18B38.3B.3B.4B3.4B10.10B$254.7B.
4BDBD15B2A2B2D17B30.2A5.7B.13B8.12B$253.15BD15B2A3BD18B30.A5.23B6.13B
$253.19B2.2B3.11B2.2B3.7B2A2B.2B27.A.AB.19B.8B2.12B$252.17B11.10B8.B.
3BA2BA3B2A27.2AB.29B.13B$248.B3.15B16.6B13.2B2A2B.B2A29.45B$247.2AB.
15B19.3B14.6B2.B30.33BD13B$247.2A18B20.B15.4B34.33B2D9BA4B$248.B.3B2A
12B20.2A14.4B35.33B2D7BABA4B$251.2B2A11B22.A15.2B38.31BD8BABA4B$252.
2B2.10B19.3A54.32BD10BA4B$251.2B3.6B.B21.A56.2A3.25B4.4B3.5B$250.B2AB
2.4B83.A3.20B4.B3.3B7.B$251.2A3.2B2AB79.3A6.15B7.2A2.B2AB5.3B$258.2A
80.A8.11B12.A3.2A6.B2AB$348.13B8.3A13.2A$347.15B7.A$347.16B$347.17B$
347.16B$349.13B$349.3B.2B2A5B$347.4B2.2B2A3B$347.2A3.8B$348.A4.2B3D3B
$345.3A5.3BD4B$345.A8.2B3D2B$354.7B$346.A7.6B$345.A.A6.6B$345.A.A6.5B
$343.3A.2A4.6B$342.A4.B6.6B$343.3AB2AB3.7B$345.A.2AB.8B$349.10B$349.
6B2A3B$349.6B2A2B5.2A$349.10B5.A$348.11B2.BA.A$348.12B.B2A$347.15B$
346.16B$343.2B.16B$342.2A18B$342.2AB.17B$343.B.4B.8B2.4B$350.7B4.4B$
351.6B5.4B$353.4B6.4B$355.3BA5.4B$356.BA.A5.4B$357.A.A6.4B$358.A8.4B$
359.3A6.4B$361.A7.4B$370.4B$286.B.B.B.B.B.B.B.B.B.C.B.B.B.B.B.B.B.B.B
.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.5B$286.16BC3BC70B$286.
21BC40B5C25B.B$286.16BC4BC39BC4BC26B2A$286.17B5C44BC26B2A$286.61BC3BC
25B2.B$287.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.
B.B.C.B.B.B.B.B.B.B.B.B.B.B.B2.2B$375.B2A$376.A.A$374.A.A.3A$374.2A5.
A$380.2A!
[[ STEP 20 ]]

A little farther afield, it seems it's almost possible to reach a 64-cell offset, and maybe slightly simpler circuitry, by adding Snarks. Here's Orthogonoid436, with a 71-cell offset, at the cost of a couple of Snarks:

x = 399, y = 216, rule = LifeHistory
140.2A$140.A.A$142.A4.2A$138.4A.2A2.A2.A$138.A2.A.A.A.A.2A$140.BABABA
.A$141.B2ABA.A$142.2B.BA$141.3B$132.2A6.4B$133.A6.B2A3B$133.A.AB3.B2A
3B$134.2AB.10B$136.13B$136.14B$116.A19.15B$114.3A21.8B2.4B$113.A24.6B
5.4B$103.2A8.2A22.9B4.4B$104.A5.5B21.4B4.2A5.4B$72.2A11.A18.A.AB.4B
22.4B5.A7.4B$71.B2AB9.A.A18.2AB.6B4.B14.4B7.3A5.3B$72.3B9.A.A20.10B.B
2A12.4B10.A6.2B$71.B.B9.2A.3A2.2A14.12B2A$71.5B8.B4.A2.A14.11B.B$71.
6B6.2AB3A3.A.AB2.4B3.13B$71.8B4.2A.A6.2A2B.5B2.12B.2B$72.13B10.24B2A$
70.13B12.24B2A$69.15B12.20B.B.B$69.15B10.B2.20B$68.17B.B5.26B$68.51B
62.A$67.13B2A11BDB2A21B50.B10.3A$66.14B2A9B3DB2A21B50.2B8.A$65.2AB3.
20BDBD23B51.3B7.2A$64.A2.A4.19BD25B51.4B3.5B$63.A.2A5.6B3.B2.2B2.29B.
B50.4B2.3B$63.A7.6B13.4B2.7B.15B51.9B7.2A$62.2A6.9B17.6B2.15B52.8B8.A
$69.4B4.2A19.3B3.10B.4B53.10B3.B.A.2A$68.4B5.A21.B4.14B54.7B2A2B.B3A
2.A$67.4B7.3A24.12B55.7B2A3BAB2.2A$66.4B10.A24.11B56.12B4A$65.4B36.
11B54.2AB.7B3.2B.A$64.4B38.9B54.A.AB.7B2.B3A$45.A17.4B6.2A3.2A26.9B
54.A5.4B4.A$45.3A14.4B6.B2AB.B2AB20.2A3.9B53.2A5.4B5.5A$48.A12.4B4.B
3.3B2.2B22.A3.9B59.4B10.A$47.2A11.4B3.4B.3B.3B23.A.A9B59.4B9.A$3.4B
13.B26.B11.13B.7B5.2A16.2A2.6B59.4B10.2A$4.4B11.3B23.3B9.23B5.A21.6B
58.4B$5.5B8.6B19.6B4.8B.19B.BA.A21.D2B2D2B56.4B$6.8B3.8B15.10B2.29B.B
2A22.B3D4B2.2A50.4B$6.19B9.2B3.44B22.4BD7BA.A48.4B203.4B$5.20B9.10B2A
3BD33B22.11B3.A48.3B205.4B$.3B.20B9.10B2A2B2D33B22.5B2A4B3.2A37.B218.
4B$.22B2A9.13B2D33B23.5B2A3B42.4B217.4B$2A21B2A9.14BD31B25.10B42.5B
217.4B$2AB.21B9.15BD32B23.9B35.2B6.2B2A2B217.4B$.B3.20B10.13B4.25B3.
2A23.9B34.10BA2BA2B217.4B$5.18B11.B4.B.7B4.B4.20B3.A25.8B33.2BA9B2A4B
217.4B$6.17B28.2A7.15B6.3A21.8B35.ABA16B.B.B.B.B.B.B119.B.B.B.B.B.B.B
.B.B.D.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.
B.5B$6.17B28.A12.11B8.A22.6B36.2A29B118.17BD3BD70B$4.19B29.3A8.13B30.
6B37.30B118.22BD40B5D25B.B$4.18B32.A7.15B29.6B39.28B118.17BD4BD39BD4B
D26B2A$4.12B2.4B39.16B29.7B37.29B118.18B5D44BD26B2A$5.11B44.17B30.6B
37.29B118.62BD3BD28B$8.8B45.16B29.6B38.16B.B.B.B.B.B.B119.B.B.B.B.B.B
.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.D.B.B.B.B.B.B.B.
B.B.B.B.B2.5B$6.10B46.13B32.5B38.14B223.B2A$6.2A2.4B.B2A.A42.5B2A2B.
3B32.6B38.13B224.A.A$7.A7.B2AB3A42.3B2A2B2.4B30.6B40.11B93.2A127.A.A.
3A$4.3A10.B4.A41.8B3.2A30.7B38.13B91.A.A127.2A5.A$4.A11.2A.3A41.3B3D
2B4.A22.A8.2B3D2B37.15B84.2A4.A135.2A$17.A.A43.4BD3B5.3A19.3A5.3BD4B
37.16B81.A2.A2.2A.4A$17.A.A43.2B3D2B8.A22.A4.2B3D3B37.17B80.2A.A.A.A.
A2.A$18.A44.7B30.2A3.8B38.16B84.A.ABABAB$64.6B7.A22.4B2.2B2A3B40.13B
85.A.AB2AB$64.6B6.A.A23.3B.2B2A5B42.2B2A5B86.AB.2B$65.5B6.A.A23.13B
42.2B2A3B91.3B$65.6B4.2A.3A19.16B40.8B91.4B6.2A$64.6B6.B4.A18.17B40.
8B88.3B2AB6.A$64.7B3.B2AB3A19.16B23.A17.8B88.3B2AB3.BA.A$65.8B.B2A.A
21.15B7.A16.3A16.7B86.10B.B2A$65.10B26.13B8.3A17.A15.7B85.13B$64.3B2A
6B18.A8.11B12.A15.2A15.6B85.14B$58.2A5.2B2A6B18.3A6.15B7.2A15.4B13.6B
84.15B19.A$59.A5.10B21.A3.20B4.B4.7B.B5.3B12.5B84.4B2.8B21.3A$59.A.AB
2.11B19.2A3.25B4.13B.4B10.6B83.4B5.6B24.A$60.2AB.12B19.32BD26B4.6B81.
4B4.9B22.2A8.2A$62.15B20.31BD21BD4B2.7B80.4B5.2A4.4B21.5B5.A$62.16B
17.33B2D18B3D4B2.6B80.4B7.A5.4B22.4B.BA.A18.A11.2A$62.16B.2B13.33B2D
2B2A15BDBD4B.7B80.3B5.3A7.4B14.B4.6B.B2A18.A.A9.B2AB$62.18B2A12.33BD
3B2A15BD15B79.2B6.A10.4B12.2AB.10B20.A.A9.3B$61.17B.B2A12.44B3.2B2.
19B114.2A12B14.2A2.3A.2A9.B.B$60.4B2.8B.4B.B11.2AB.29B2.10B11.17B114.
B.11B14.A2.A4.B8.5B$59.4B4.7B17.A.AB.19B.8B4.6B16.15B3.B112.13B3.4B2.
BA.A3.3AB2A6.6B$58.4B5.6B18.A5.23B9.3B19.15B.B2A109.2B.12B2.5B.2B2A6.
A.2A4.8B$57.4B6.4B19.2A5.7B.13B11.B20.18B2A108.2A24B10.13B$56.4B5.A3B
29.3B.3B.4B4.3B11.2A20.12B2A3B.B109.2A24B12.13B$55.4B5.A.AB29.2B2.3B
3.B4.4B12.A22.11B2A2B113.B.B.20B12.15B$54.4B6.A.A29.B2AB.B2AB7.2A15.
3A19.10B2.2B117.20B2.B10.15B$53.4B8.A31.2A3.2A9.A17.A21.B.6B3.2B115.
26B5.B.17B$52.4B6.3A45.3A44.4B2.B2AB50.A62.51B$51.4B7.A47.A45.B2A2B3.
2A51.3A10.B50.21B2ABD11B2A13B$50.4B103.2A61.A8.2B50.21B2AB3D9B2A14B$
219.2A7.3B51.23BDBD20B3.B2A$219.5B3.4B51.25BD19B4.A2.A$221.3B2.4B50.B
.29B2.2B2.B3.6B5.2A.A$211.2A7.9B51.15B.7B2.4B13.6B7.A$211.A8.8B52.15B
2.6B17.9B6.2A$208.2A.A.B3.10B53.4B.10B3.3B19.2A4.4B$208.A2.3AB.2B2A7B
54.14B4.B21.A5.4B$209.2A2.BA3B2A7B55.12B24.3A7.4B$211.4A12B56.11B24.A
10.4B$211.A.2B3.7B.B2A54.11B36.4B$212.3AB2.7B.BA.A54.9B38.4B$215.A4.
4B5.A54.9B26.2A3.2A6.4B17.A$210.5A5.4B5.2A53.9B3.2A20.B2AB.B2AB6.4B
14.3A$210.A10.4B59.9B3.A22.2B2.3B3.B4.4B12.A$212.A9.4B59.9BA.A23.3B.
3B.4B3.4B11.2A$211.2A10.4B59.6B2.2A16.2A5.7B.13B11.B26.B13.4B$33.4B
187.4B58.6B21.A5.23B9.3B23.3B11.4B$32.4B189.4B56.2B2D2BD21.A.AB.19B.
8B4.6B19.6B8.5B$226.4B50.2A2.4B3DB22.2AB.29B2.10B15.8B3.8B$30.4B193.
4B48.A.A7BD4B22.44B3.2B9.19B$29.4B195.3B48.A3.11B22.33BD3B2A10B9.20B$
28.4B208.B37.2A3.4B2A5B22.33B2D2B2A10B9.20B.3B$27.4B207.4B42.3B2A5B
23.33B2D13B9.2A22B$26.4B207.5B42.10B25.31BD14B9.2A21B2A$25.4B207.2B2A
2B6.2B35.9B23.32BD15B9.21B.B2A$24.4B207.2BA2BA10B34.9B23.2A3.25B4.13B
10.20B3.B$23.4B207.4B2A9BA2B33.8B25.A3.20B4.B4.7B.B4.B11.18B$22.5B.B.
B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.D.B.B.B
.B.B.B.B.B.B109.B.B.B.B.B.B.16BABA35.8B21.3A6.15B7.2A28.17B$20.70BD3B
D17B108.29B2A36.6B22.A8.11B12.A28.17B$17.B.25B5D40BD22B108.30B37.6B
30.13B8.3A29.19B$16.2A26BD4BD39BD4BD17B108.28B39.6B29.15B7.A32.18B$
16.2A26BD44B5D18B108.29B37.7B29.16B39.4B2.12B$17.28BD3BD62B108.29B37.
6B30.17B44.11B$16.5B2.B.B.B.B.B.B.B.B.B.B.B.B.D.B.B.B.B.B.B.B.B.B.B.B
.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B109.B.B.B.B.B.B.16B38.6B29.
16B45.8B$19.2AB213.14B38.5B32.13B46.10B$18.A.A214.13B38.6B32.3B.2B2A
5B42.A.2AB.4B2.2A$16.3A.A.A212.11B40.6B30.4B2.2B2A3B42.3AB2AB7.A$15.A
5.2A211.13B38.7B30.2A3.8B41.A4.B10.3A$15.2A216.15B37.2B3D2B8.A22.A4.
2B3D3B41.3A.2A11.A$232.16B37.4BD3B5.3A19.3A5.3BD4B43.A.A$231.17B37.3B
3D2B4.A22.A8.2B3D2B43.A.A$232.16B38.8B3.2A30.7B44.A$233.13B40.3B2A2B
2.4B22.A7.6B$233.5B2A2B42.5B2A2B.3B23.A.A6.6B$235.3B2A2B42.13B23.A.A
6.5B$235.8B40.16B19.3A.2A4.6B$234.8B40.17B18.A4.B6.6B$234.8B17.A23.
16B19.3AB2AB3.7B$234.7B16.3A16.A7.15B21.A.2AB.8B$234.7B15.A17.3A8.13B
26.10B$235.6B15.2A15.A12.11B8.A18.6B2A3B$235.6B13.4B15.2A7.15B6.3A18.
6B2A2B5.2A$236.5B12.3B5.B.7B4.B4.20B3.A21.10B5.A$236.6B10.4B.13B4.25B
3.2A19.11B2.BA.A$235.6B4.26BD32B19.12B.B2A$235.7B2.4BD21BD31B20.15B$
236.6B2.4B3D18B2D33B17.16B$236.7B.4BDBD15B2A2B2D33B13.2B.16B$235.15BD
15B2A3BD33B12.2A18B$235.19B2.2B3.44B12.2AB.17B$234.17B11.10B2.29B.B2A
11.B.4B.8B2.4B$230.B3.15B16.6B4.8B.19B.BA.A17.7B4.4B$229.2AB.15B19.3B
9.23B5.A18.6B5.4B$229.2A18B20.B11.13B.7B5.2A19.4B6.4B$230.B.3B2A12B
20.2A11.3B4.4B.3B.3B29.3BA5.4B$233.2B2A11B22.A12.4B4.B3.3B2.2B29.BA.A
5.4B$234.2B2.10B19.3A15.2A7.B2AB.B2AB29.A.A6.4B$233.2B3.6B.B21.A17.A
9.2A3.2A31.A8.4B$232.B2AB2.4B44.3A45.3A6.4B$233.2A3.2B2AB45.A47.A7.4B
$240.2A103.4B21$366.4B$367.4B$368.4B$369.4B$370.4B$371.4B$372.4B$288.
B.B.B.B.B.B.B.B.B.C.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B
.B.B.B.B.B.B.B.5B$287.17BC3BC70B$287.22BC40B5C25B.B$287.17BC4BC39BC4B
C26B2A$287.18B5C44BC26B2A$287.62BC3BC28B$287.B.B.B.B.B.B.B.B.B.B.B.B.
B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.C.B.B.B.B.B.B.B.B.B.B.B.B2.5B
$377.B2A$378.A.A$376.A.A.3A$376.2A5.A$382.2A!
[[ STEP 20 ]]

... or Orthogonoid459 -- a 69-cell offset, with only one Snark:

x = 439, y = 211, rule = LifeHistory
171.A$170.A.A$170.A.A$168.3A.2A11.A$167.A4.B10.3A$142.2A11.A12.3AB2AB
7.A$141.B2AB9.A.A13.A.2AB.4B2.2A$142.3B9.A.A17.10B$141.B.B9.2A.3A15.
8B$141.5B8.B4.A14.11B$141.6B6.2AB3A9.4B2.12B$141.8B4.2A.A11.18B$142.
13B12.19B$140.13B14.17B$126.A12.15B13.17B$124.3A12.15B10.B2.18B$123.A
14.17B.B5.23B3.B$113.2A8.2A13.48B.B2A$114.A5.5B12.13B2A11BDB2A21B2A$
82.2A11.A18.A.AB.4B13.14B2A9B3DB2A22B$81.B2AB9.A.A18.2AB.6B4.B5.2AB3.
20BDBD21B.3B$82.3B9.A.A20.10B.B2A3.A2.A4.19BD23B$81.B.B9.2A.3A2.2A14.
12B2A2.A.2A5.6B3.B2.2B2.26B12.A$81.5B8.B4.A2.A14.11B.B3.A7.6B13.4B2.
7B3.8B10.3A$81.6B6.2AB3A3.A.AB2.4B3.13B4.2A6.9B17.6B8.5B8.A$81.8B4.2A
.A6.2A2B.5B2.12B.2B9.4B4.2A19.3B11.4B7.2A$82.13B10.24B2A16.A21.B13.4B
3.5B$80.13B12.24B2A17.3A33.4B2.3B$79.15B12.20B.B.B20.A34.9B7.2A$79.
15B10.B2.20B8.B50.8B8.A$78.17B.B5.26B6.2B51.10B3.B.A.2A$78.51B4.3B51.
7B2A2B.B3A2.A$77.13B2A11BDB2A21B4.4B51.7B2A3BAB2.2A$76.14B2A9B3DB2A
21B3.4B52.12B4A$75.2AB3.20BDBD23B3.4B51.2AB.8B2.2B.A$74.A2.A4.19BD25B
2.4B51.A.AB.7B2.B3A$73.A.2A5.6B3.B2.2B2.29B.4B52.A5.5B3.A$73.A7.6B13.
4B2.7B.17B52.2A5.4B5.5A$72.2A6.9B17.6B2.16B59.4B10.A$79.4B4.2A19.3B3.
10B.4B59.4B9.A$78.4B5.A21.B4.14B73.2A$77.4B7.3A24.12B$76.4B10.A24.11B
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405.B2A$406.A.A$404.A.A.3A$404.2A5.A$410.2A!
[[ STEP 20 ]]

Unfortunately I'm fairly sure that Golly will be much much happier with a design that uses only pure powers of two, spatially and temporally, so it seems better to stick with something like Orthogonoid496 in spite of the higher object count.
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dvgrn
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Re: Orthogonoid working notes

Postby dvgrn » June 7th, 2017, 10:00 am

A wild thought that came up this morning, thinking about the Orthogonoid325 blueprint that I really should have posted on this thread:

The assumption has always been that identical glide-reflected constructor arms can only build orthogonal or diagonal self-constructing spaceships. But is that really true?

Let's say we want the left-side constructor arm in an Orthogonoid to build its child constructor arm at (2,-128). That part's easy, we can just compile it that way. But if the right side does the same, we get a shrinking spacehip, which is going to be in big trouble eventually...! So the right-side constructor arm has to build at (2,-128) also. In the mirror-image world of the right side, that looks like (-2,-128).

If the elbow block were somehow magically moved 2fd farther away on each Orthogonoid right-side constructor, and the target hand block were moved four cells over from its (2,-128) location, then the construction would occur in the right place, the destruction would still work the same, and I think we'd end up with a self-constructing oblique spaceship with a new-record minimum height of 300-odd cells.

Along somewhat similar lines as the convergent destruction recipe idea -- what's the simplest way to leave some junk lying around on one side, but not the other, that results in

1) the elbow moving (2X,-2X);
2) a target hand moving (4X,0);
3) the junk moving (4X,-128) so that it can do the same arm-adjusting trick for the next child constructor arm?

Probably most or all of the required adjustment mechanism would always be constructed. In the presence/absence of some key piece, it would perform the arm adjustment. In the absence/presence of the key piece, it would all self-destruct without doing anything. The left-side construction arm ends up doing a complicated NOP operation, and the right-side arm gets the minor adjustment it needs.

It seems to me that this is definitely possible one way or another, but I haven't come up with a really clever way to go about it yet. Any suggestions?
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