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Glider pair adjustment toolkit

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Glider pair adjustment toolkit

Postby dvgrn » March 12th, 2017, 6:34 pm

Related to the optimization problems that have been coming up in the Construction practice thread recently --

The script that chris_c wrote to automatically produce "well-separated" synchronized salvos from a single input glider, needs a total of nine different mechanisms -- 180-degree (0|+4) color changers and color preservers (the "A" and "B" components, and 180-degree (0|1|2|3) adjusters (the "C" components) -- plus a single type of glider splitter.

This produces very workable but somewhat unwieldy "ladder" structures. The choice of H-to-2G splitter means that the ladder narrows toward the far end, and usually the limited space there constrains the width of the entire ladder. When the output gliders are feeding multiple edge shooters in a shotgun, you have to move the 180-degree pieces to their widest adjustment at the narrow end of the ladder, to allow the first constructed gliders enough time to catch up. That leaves a lot of space at the upper end.

It might work a lot better to switch to a different H-to-2G, choosing maybe the fastest possible 0-degree output that stays on the same diagonal as the input, more or less. Could be worth investigating that.

What I've been working on is a different idea. The two 180-degree reflectors are overkill -- you end up with two different places where you can move a reflector to adjust by +/-8N, where you really only need one. I think that a significantly more compact toolkit can be designed, using a variety of H-to-2G splitters, and making connections to the outputs with Snark chains and nothing else.

EDIT: Improved classifier script, works with two gliders in any orientation:

# Hto2Gclassifier_v1.1.py
# -- given any two selected gliders,
#    display the class of Herschel-to-2-glider converter
#    that produces those two synchronized gliders,
#    with the help of some number of Snark reflectors
import golly as g

equivdict={"NW":[0,0,0],"NE":[2,0,1],"SE":[0,1,1],"SW":[2,1,0]}
gliders=["NW0:3o$o$bo!","NW1:bo$2o$obo!","NW2:2o$obo$o!","NW3:b2o$2o$2bo!",
         "NE0:b2o$obo$2bo!","NE1:2o$b2o$o!","NE2:3o$2bo$bo!","NE3:bo$b2o$obo!",
         "SE0:bo$2bo$3o!","SE1:obo$b2o$bo!","SE2:2bo$obo$b2o!","SE3:o$b2o$2o!",
         "SW0:o$obo$2o!","SW1:2bo$2o$b2o!","SW2:bo$o$3o!","SW3:obo$2o$bo!"]
gdict={}
for item in gliders:
  name,rle = item.split(":")
  gdict[name]=g.parse(rle)

def findglider(clist):
  canonical = g.transform(clist,-clist[0],-clist[1])
  canoncoords = zip(canonical[0::2],canonical[1::2])
  for key in gdict:
    glist = g.transform(gdict[key],-gdict[key][0],-gdict[key][1])
    gcoords = zip(glist[0::2],glist[1::2])
    match=1
    for coord in gcoords:
      if coord not in canoncoords:
        match=0
        break
    if match==1:
      for coord in gcoords:  # remove the matching glider
        canoncoords.remove(coord)
      # return UL bounding box corner of matching glider
      x, y = min(glist[0::2])+clist[0],min(glist[1::2])+clist[1]
      dir,phase = key[:2],int(key[2])
      outlist=[]
      for a,b in canoncoords: outlist+=[a,b]
      return [dir,phase,x,y],g.transform(outlist,clist[0],clist[1])

def findgliders(clist):
  # check the top left cell in clist against the first cell in each gdict[key]
  stats1,remainder=findglider(clist)
  stats2,empty=findglider(remainder)
  if empty!=[]: g.exit("Could not recognize gliders in selection.")
  return stats1, stats2

# find an {outdir}-traveling glider equivalent to one with the statistics in statlist
def findcanonical(statslist,outdir):
  dir,phase,x,y = statslist
  dphase, dx, dy = equivdict[dir]
  dphaseout, dxout, dyout = equivdict[outdir]
  # this is really all two-state arithmetic, so + vs. - below doesn't actually matter
  return [outdir, (phase+dphase-dphaseout)%4, x+dx-dxout, y+dy-dyout]
 
if g.numstates()!=2: g.exit("Please convert to standard two-state Life before running this script.")
clist = g.getcells(g.getselrect())
if len(clist)!=20:  g.exit("Please select a rectangle containing the two gliders to be synchronized, and nothing else." \
                         + "\nThere should be at least a four-cell gap between the gliders horizontally and vertically.")
while 1:  # iterate until we find NW0
  stats1, stats2 = findgliders(clist)
  canonical1 = findcanonical(stats1,"NW")
  canonical2 = findcanonical(stats2,"SE")
  if canonical1[1]==0: break
  clist = g.evolve(clist,1)

dir1,phase1,x1,y1 = canonical1
dir2,phase2,x2,y2 = canonical2
charx = "E" if (x1-x2)%2 else "O"  # looks backwards -- the usual fencepost issue
chary = "e" if (y1-y2)%2 else "o"  # (bounding box coords vs. # of cells in bounding box width)
rating = charx+chary+str(phase2)

clist = g.getcells(g.getselrect())
while 1:  # iterate until we find NW0
  stats1, stats2 = findgliders(clist)
  stats2mod = stats2[:]
  stats2mod[2]-=1024
  stats2mod[3]-=1024 # shouldn't matter, but it seems to!
  reversed1 = findcanonical(stats1,"SE")
  reversed2 = findcanonical(stats2mod,"NW")
  if reversed2[1]==0: break
  clist = g.evolve(clist,1)

dirr1,phaser1,xr1,yr1 = reversed1
dirr2,phaser2,xr2,yr2 = reversed2
charrx = "E" if (xr1-xr2)%2 else "O"
charry = "e" if (yr1-yr2)%2 else "o"
ratingr = charrx+charry+str(phaser1)

g.note(rating + " if the first glider in the selection (reading from top down and left to right) is the reference glider\n" \
     + ratingr + " if the second glider is the reference glider (i.e., it will be connected to the NW output in the stamp collection)")

I had gone through the first third of the H-to-G reference collection -- output lanes -20 to +19 -- using this previous version of the classifier script, which required that the gliders be moving NW and SE in the appropriate corners of their shared bounding box:

import golly as g
r=g.getrect()
if len(r)==0: g.exit("No H-to-2G pattern to classify.")
clist = g.getcells(r)
if len(clist)%2: g.exit("Use two-state rule B3/S23 to avoid voiding the warranty..")

g.run(4096)
r=g.getrect()
xmin, ymin, xmax, ymax = r[0], r[1], r[2]+r[0]-1,r[3]+r[1]-1
# the four cells below are always on in any phase of NW and SE gliders,
#  if those gliders have reached the corners of the bounding box
# -- so this is only guaranteed to work if there are no other gliders in the pattern
# Or other spaceships, puffers, etc. Works as long as it's a H-to-2G NW and SE.
if g.getcell(xmin,ymin+1)==0 or g.getcell(xmin+1,ymin)==0 or g.getcell(xmax,ymax-1)==0 or g.getcell(xmax-1,ymax)==0:
  g.exit("Please start with an H-to-2G, gliders pointing NW and SE.")

count = 0

while 1:
  if count==4: g.exit("There's something weird in the NW corner.")
  if g.getcell(xmin, ymin)==1 and g.getcell(xmin+1, ymin)==1 and g.getcell(xmin+2, ymin)==1 \
     and g.getcell(xmin, ymin+1)==1 and g.getcell(xmin+1, ymin+2)==1: break
  count+=1
  g.run(1)
  r=g.getrect()
  xmin, ymin, xmax, ymax = r[0], r[1], r[2]+r[0]-1,r[3]+r[1]-1

idstring = "E" if r[2]%2==0 else "O"
idstring+="e" if r[3]%2==0 else "o"
# EXEY, EXOY, OXEY, OXOY
if g.getcell(xmax-1, ymax-2)==1: idstring+="0"
elif g.getcell(xmax-1, ymax-1)==1 and g.getcell(xmax, ymax-2)==1: idstring+="1"
elif g.getcell(xmax-2, ymax-1)==1: idstring+="2"
else: idstring+="3"
# could not be so lazy, and check all five cells in each case
# -- but what kind of weirdness would cause false positives here, really?
# g.setclipstr(idstring+" (count = "+str(count)+")")
g.show(idstring+" (count = "+str(count)+")")

The new script gives the same ratings for all the H-to-2Gs in the toolkit so far (except I caught a couple of mistakes, now corrected in the stamp-collection pattern in the next post).

There are sixteen distinct ways for output gliders to be produced in relation to each other, such that you can't convert from one class to another by adding Snarks. The script isn't set up to care how long it takes to produce the gliders from an input signal -- only the relative placement of the outputs matters.

I labeled the sixteen types [E|O][e|o][0|1|2|3], where the output gliders are reflected so they're traveling away from each other, one heading northwest and one southeast, and the NW glider is in 3o$o$bo! orientation.

  • E = bounding box around the two gliders has even width
  • O = bounding box around the two gliders has odd width
  • e = bounding box around the two gliders has even height
  • o = bounding box around the two gliders has odd height
  • 0 = SE glider is bo$2bo$3o!
  • 1 = SE glider is obo$b2o$bo!
  • 2 = SE glider is 2bo$obo$b2o$
  • 3 = SE glider is o$b2o$2o!
There are good alternative labels for the sixteen types -- in particular, we could have SameColor0..7 and DifferentColor0..7. Eo0..3 is equivalent to Oe4..7 (or vice versa) and similarly Ee0..3 would be the same as Oo4..7.

I chose this classification because it seemed easier to distinguish the classes with a just few manual steps in Golly:

  • select two gliders that are moving away from each other, with one glider in the NW corner;
  • hit 's' to shrink the bounding box;
  • check width and height to get the E/O and e/o part (even vs. odd width and height respectively);
  • look at the SE glider to decide the 0, 1, 2, or 3 part. 0 would be a 180-degree rotated copy of the NW glider.

Or you can just paste the gliders into a new layer and run the above script.

Which glider you put in the NW corner depends on which side of the gliders you want your G-to-2G to be on. The script assumes that the source signal is coming from the W, SW, or S. If your Herschel is coming in from some other direction, either the output signals may have to cross output signals, or the output signals may have to cross each other. This is perfectly possible but often causes minor trouble with the circuit's repeat time.

An odd artifact of the classification scheme is that some H-to-2Gs are in the same class with their mirror images, but some change classes if you reflect them. Specifically:

Oe2 <--> Eo2
Ee1 <--> Eo3
Eo1 <--> Ee3
Oe1 <--> Oo3
Oo1 <--> Oe3

Even more complicated things happen with rotations. In some cases, a clockwise rotation of the H-to-2G doesn't change the class, but a counterclockwise rotation does. Other equivalence classes are invariant under both rotation and reflection. If this seems weird, just think about how weird gliders are -- it will all make sense eventually.

I'll put a complete table here eventually. Meanwhile, here are the equivalence classes that are related to each other via rotation and reflection:

Oo0 (never changes)
Oo1/Ee1/Oe3/Eo3
Oo2/Ee2
Oo3/Oe1
Oe0/Eo0
Oe1: see Oo3
Oe2/Eo2
Oe3: see Oo1
Eo0: see Oe0
Eo1/Ee3
Eo2: see Oe2
Eo3: see Oo1
Ee0 (never changes)
Ee1: see Oo1
Ee2: see Oo2
Ee3: see Eo1
dvgrn
Moderator
 
Posts: 3996
Joined: May 17th, 2009, 11:00 pm
Location: Madison, WI

Re: Glider pair adjustment toolkit (continued)

Postby dvgrn » March 12th, 2017, 6:36 pm

Code: Select all
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#C [[ VIEWONLY THUMBNAIL THUMBSIZE 2 X 0 Y -1 ZOOM 3 ]]

Here's the rough stamp collection I've come up with so far. I stopped running the classifier as soon as I had examples of all sixteen output classes. More soon.

It's fairly usable already. I was able to finish off the glider-to-c/3 converter using this collection, collecting four synchronized gliders into one glider fairly quickly and without any synchronization mistakes.

EDIT: Updated 4/30/2017, fixed two classification mistakes.
x = 1310, y = 833, rule = LifeHistory
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7D4.6D11.6D113.AB.2B203.6D23.6D10.6D244.18D11.7D11.6D$149.7D13.7D3.7D
10.7D207.7D13.7D3.7D11.6D116.3B202.6D22.7D10.7D243.18D11.6D11.7D$149.
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18D11.6D10.7D$149.6D15.6D3.6D12.6D207.6D15.6D3.6D11.7D114.3B2AB6.A
194.18D10.6D12.6D243.18D11.23D$149.6D15.6D3.6D12.6D207.6D15.6D3.6D10.
7D114.4B2AB3.BA.A194.18D10.6D12.6D243.18D11.22D$149.6D15.6D3.5D14.5D
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3.5D14.5D207.6D15.6D3.22D113.13B197.18D10.5D14.5D243.6D23.20D$149.6D
15.6D3.5D14.5D207.6D15.6D3.21D113.14B197.18D10.5D14.5D243.6D23.9D$
149.7D13.7D3.5D14.5D207.7D13.7D3.20D113.15B197.6D22.5D14.5D243.6D23.
8D$149.7D13.7D3.6D12.6D207.7D13.7D3.9D123.4B2.8B199.6D22.6D12.6D243.
6D23.7D$149.7D13.6D4.6D12.6D207.7D13.6D4.8D123.4B5.6B199.6D22.6D12.6D
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12.6D243.6D24.6D$150.7D11.7D4.7D10.7D208.7D11.7D4.7D124.2B5.2A4.4B
197.6D22.7D10.7D243.6D24.6D10.4D$151.6D11.6D6.6D10.6D210.6D11.6D6.6D
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152.7D7.7D8.7D6.7D212.7D7.7D7.7D8.6D91.3A10.2B8.A10.4B194.6D15.4D5.7D
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14D$154.17D12.16D216.17D11.18D94.5B3.4B218.25D7.16D247.25D11.9D$156.
13D16.12D220.13D15.14D98.3B2.4B219.25D9.12D$158.9D21.6D225.9D19.9D91.
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$561.4B27.9B7.2A$591.4B2.3B$590.4B3.5B$589.4B7.2A$565.4B20.3B8.A$566.
4B10.A8.2B10.3A$567.4B7.3A8.B13.A$568.4B5.A7.B$569.4B4.2A5.2B$570.9B
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3D4.D6.D2.D.D.D$569.14B97.D.D7.D3.D3.D3.D5.D3.2D2.D$569.13B94.D3.D.D
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682.4B11.8B.BA.A$683.4B2.4B3.9B.B2A264.3D2.D3.D.5D.5D3.D4.3D3.3D$684.
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2D2.D35.D3.D.2D.2D3.D3.D3.D3.D5.D5.D3.D3.D$678.B2AB3CB2A25B365.D3.D.
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3D36.D3.D.D5.D7.D3.D3.D.D3.D$369.D3.D.D.D.D5.D3.D5.D5.D5.D3.2D2.D273.
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4.D4.3D2.5D2.3D280.2A3.8B56.D2.2D.3D5.D5.D3.D2.D3.4D280.3D2.3D6.D5.D
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2AB.10B35.D5.D8.D4.D5.D4.D.D83.A3.4B26.4B69.A11.A2.11B54.4B10.2B2A.A
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4B22.4B74.A7.16B2A53.4B6.7B$373.D.D.D.D9.D5.D5.D5.D49.D3.D.5D2.3D4.D
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6.4B75.8B2.16B51.2A3.4B.8B$370.3D2.D3.D7.5D3.D3.5D2.3D270.D3.D.D7.D5.
D3.5D5.D82.28B151.11B7.A8.4B78.22B54.A4.12B$679.D3.D.D7.D5.D6.D6.D81.
29B152.5BC5B6.2A6.4B79.22B54.A.AB2.11B.2B$679.D3.D.5D2.3D4.D6.D3.3D
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14B.2B$795.16B.6B8.2A38.4B107.24B78.2BC14B4.4B60.13B$792.14B.B5.B2.B
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52.18B.B2A$785.A.AB2.15B9.2A53.4B108.22B73.11B7.A8.4B51.2BC15B2.B$
696.A.2A86.2AB.15B66.4B105.8B2.16B70.4B3.4B9.3A6.4B49.3BCBC4B.8B$681.
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6B$467.2A173.5D10.3D22.5BC4B4.2B2A3.2A4.3A74.24B61.10BA105.3A4.9B69.
3A3.4B28.4B41.4B12.7B$465.2B2AB172.D13.D3.D22.2B3C4B2.3B.B4.B4.A75.
25B61.12B2A103.A7.6B71.A4.4B30.4B39.4B13.7B$465.4B173.D7.3D3.D2.2D21.
3BCBC4B.7B2.2B4.2A74.2BC13B.10B59.11B2.A107.A.2AB.3B76.4B32.4B37.4B
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9B4.A106.3AB2AB2.4B111.2B37.4B15.5B$465.6B171.D6.D3.D2.2D2.D22.25B76.
2B3C4B2.3B.B4.B4.A49.2A8.9B5.3A102.A4.B6.2A112.B36.4B16.4B$467.5B170.
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4B17.B.2B$449.4B13.6B170.5D3.3D4.3D27.22B73.10B4.BA2.A4.A6.A47.A.AB4.
10B113.A.A7.3A146.3B18.B2A$8.9D434.3B12.7B215.20B73.4B12.3A4.A56.2AB.
14B112.A.A9.A146.2B20.2A$6.13D432.4B11.7B214.20B73.4B20.2A57.17B112.A
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7B213.2AB.15B74.4B15.A.2A63.17B$4.7D3.7D433.2B3C4B2.7B19.2A191.A.AB2.
15B9.2A61.4B82.17B.B$3.7D5.7D431.3BCBC4B.8B12.2B5.A192.A5.15B8.B2AB
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23B52.A.AB11.2A155.A7.18BA.A65.4AB$9.7D133.4B11.10B43.2BC13B4.BA.A
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$158.A.AB4.14B63.4B160.A4.4B6.6B52.4B6.11B8.3A12.B.3B.B43.29B2.2B.BAB
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157.2A8.13B65.4B155.A5.4B7.8B49.4B6.B2AB3.6B69.19B2.12B7.2B91.23B.2A.
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3D2.5D3.D4.3D2.5D3.D4.3D3.3D$223.B528.D2.2D.D.D.D3.D5.D5.D5.D5.2D2.D.
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3.D7.D4.2D3.D3.D.D3.D$222.2B528.D3.D.D.D.D3.D4.D6.D5.D7.D.2D2.D37.3BC
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206.A12.4B616.17B4.4B137.D3.D.2D.2D3.D3.D3.D3.D5.D3.D3.D.D3.D31.D3.D.
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10.7B542.3BCBC4B.9B236.16B62.2B3C4B2.10B$192.4B12.6B543.2B3C4B2.7B
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4.3D3.3D149.4B12.A241.2B3C4B2.6B69.18B3A$186.2B17.A286.D3.D.D3.D2.3D
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3D4.D4.3D3.3D2.5D400.4B22.A59.3AB2AB2.10B$492.D3.D.D3.D2.3D3.3D4.D4.
3D2.5D2.3D463.4B23.2A57.A4.B4.12B$1000.4B84.3A.2A4.5B4.2A.A$999.4B87.
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4B6.4B97.19B2A33.2B23.2A7.B2.4B$391.4B6.4B96.19B.B2A33.3B22.A6.8B$
391.3B6.4B95.19B4.B34.4B18.BA.A4.9B$391.2B106.2BC16B40.4B14.2A.B2A5.
8B$391.B106.3BCBC4B.9B41.4B12.B2A2B6.8B$499.2B3C4B2.7B43.10B6.4B5.10B
$498.5BC4B2.7B44.5BC4B3.6B5.9B$497.10B4.6B45.2B3C4B2.6B7.7B8.2A$496.
4B10.7B45.2BCBC4B.7B5.9B7.B2AB$495.4B12.6B45.2BC15B3.11B7.2B$494.4B
13.7B44.19B2.12B7.2B$494.2A16.5B47.30B6.2B2AB$495.A16.6B48.29B2.2B.BA
B.A$492.3A15.9B48.33B.A.A$492.A17.2A.7B46.33BA.A.A.A$145.3D2.5D8.3D2.
5D4.D2.5D326.A5.4B45.32BABA.A.A.A$144.D3.D.D11.D3.D3.D5.2D6.D323.3A7.
4B42.2AB.3B2.23B2.BA2.A2.A$144.D5.D15.D3.D4.D.D5.D324.A10.4B40.A.AB6.
22B4.B2A.2A$145.3D2.3D3.5D4.D4.D3.D2.D4.D337.4B39.A8.24B5.A.A$148.D.D
13.D5.D3.5D2.D339.4B37.2A7.24B6.A.A$144.D3.D.D12.D6.D6.D2.D341.4B44.
10B4.9B9.A$145.3D2.5D7.5D3.D6.D2.D179.D3.D.D3.D2.3D2.5D3.D4.3D2.5D
122.4B42.2A2B.6B6.7B$360.2D2.D.D3.D.D3.D3.D4.2D3.D3.D.D127.4B40.ABAB
3.B.B7.9B$360.D.D.D.D3.D5.D3.D5.D7.D.D128.4B38.BA2B5.3B6.10B$360.D2.
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4.2D3.D3.D93.4B7.2A9.8B$360.D3.D.2D.2D.D3.D3.D5.D3.D3.D.D3.D24.D.D.D.
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2.2D.D.D.D3.D4.3D4.D5.D5.D5.2D92.4B22.8B$425.D3.D.D.D.D3.D7.D3.D5.D5.
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425.D3.D.D3.D2.3D3.3D4.D4.3D3.3D3.3D89.4B32.4B$559.4B34.4B$558.4B36.
4B$557.4B38.4B$426.3D2.5D.5D.5D2.3D3.3D141.4B90.3D2.D3.D2.3D2.5D2.3D
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3.D161.D5.D3.D.D3.D3.D3.D3.D.D60.3D2.5D.5D.5D2.3D3.3D$361.4B61.3D2.3D
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166.D.D.D.D.D3.D3.D3.D3.D.D3.D55.D5.D5.D7.D7.D5.D$363.4B58.D3.D.D5.D
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3D2.3D4.3D4.D6.D4.2D$364.4B50.4B4.3D2.5D2.3D4.D3.5D2.3D38.D3.D.D5.D3.
D3.D4.D4.D3.D162.3D2.D3.D2.3D4.D4.3D3.3D60.D.D9.D3.D5.D7.D$365.4B50.
4B75.3D2.5D2.3D4.D3.5D2.3D252.D3.D.D5.D3.D3.D4.D4.D3.D$366.4B50.4B
360.3D2.5D2.3D4.D3.5D2.3D$367.4B16.2A32.4B$368.4B14.B2A2B3.2A26.4B$
369.4B14.4B2.B2AB26.4B$9.8D152.4B197.4B9.B.6B3.2B28.4B$7.13D148.4B
199.4B6.10B2.2B30.4B$5.16D146.4B201.4B5.11B2A2B30.4B18.A$4.18D144.4B
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14B.2B73.4B36.D3.D.D5.D7.D3.D3.D.D3.D88.2B3C13B10.8B3.2B2A15B2A46.18B
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87.3BCBC4B.7B13.8B.17B.B2A44.18B.B2A$7.9D132.4B3C4B2.7B199.4B17.7B35.
18B.B2A62.A7.4B39.3D2.3D4.3D4.D6.D4.2D89.2BC15B12.26B2.B45.2BC15B2.B$
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5D10.3D31.22BD15B59.10B3.7B$.9D9.4D125.21B196.B23.14B25.10B3.7B69.6B.
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4B2.7B41.4B75.5D3.3D3.5D26.A19.4B6.4B2.5B54.4B16.6B200.D3.D.D6.D6.D5.
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3.D.D3.D28.D2.2D.3D4.4D3.D5.2D4.D$150.2A16.A.3A250.A16.2AB.5B55.3BCBC
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7.D4.3D3.3D3.3D29.D3.D.D9.D3.D7.D3.D$166.A.A4.A265.A.AB3.4B55.2BC15B
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2BA3B.B2A45.4B16.2A8.4B265.D3.D.5D2.3D4.D4.3D3.3D$171.A.A.2A261.2A8.
4B55.18B2A42.4B10.A.A.A.2A114.A7.4B5.BA2BAB4.B46.3B28.4B$171.A.A.2A
272.4B56.14B.2B44.4B10.2B2A.A2.A119.4B8.2AB52.2B30.4B$172.A277.4B56.
13B48.4B10.4B2.2A118.4B10.2B52.B32.4B$451.4B54.14B49.4B6.7B121.4B99.
4B$452.4B53.14B50.4B3.8B121.4B$453.4B50.2AB.3B.8B46.2A3.4B.8B121.4B$
454.4B48.A.AB6.7B47.A4.12B120.4B$455.4B47.A10.4B49.A.AB2.11B.2B117.3B
307.2A$456.4B45.2A10.2B2AB49.2AB.14B2A116.2B306.2B2AB$519.2A52.16B2A
116.B307.4B$573.14B.2B425.6B$574.13B428.6B$426.D3.D.5D2.3D2.5D2.3D
119.14B.2B427.5B$426.2D2.D.D5.D3.D3.D3.D3.D116.18B2A425.6B$426.D.D.D.
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3.D.D5.D3.D3.D3.D3.D114.2B3C4B2.7B416.5BC4B2.7B$426.D3.D.5D2.3D4.D4.
3D114.5BC4B2.7B105.D3.D.D3.D3.D4.3D2.5D3.D4.3D3.3D266.2B3C4B2.7B50.4B
$567.10B3.7B105.2D2.D.D3.D2.2D3.D3.D3.D4.2D3.D3.D.D3.D264.3BCBC4B.8B
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3.D5.D3.2D2.D3.D269.18B2A50.5BC4B7.2A6.3A$420.4B140.2A15.6B.B103.D3.D
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422.4B136.3A16.6B421.14B.2B3.3A46.2BC14B4.4B2.2A$423.4B23.2A110.A16.
2AB.5B420.16B2A5.A45.23B4.A$424.4B22.A127.A.AB3.4B196.D3.D.5D2.3D2.5D
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D52.D.D.D.D5.D3.D3.D7.D191.A7.9B10.3B.BA.A42.20B$427.4B12.B2A2B140.4B
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2A6.10B8.5B.B2A43.20B$428.10B6.4B6.A134.4B99.D2.2D.3D5.D3.D.D.D3.D3.D
2.D4.2D53.D3.D.D5.D3.D3.D7.D145.D13.D3.D34.10B7.8B43.8B2.13B$429.5BC
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12B44.A7.15BA.A$429.3BCBC4B.7B4.2A139.4B96.D3.D.5D2.3D3.3D4.D6.D3.3D
227.D6.5D4.D37.23B.2B39.3A8.2A3.8B.2BA$430.2BC15B.4B140.4B362.D6.D7.D
38.28B37.A11.A2.10B.B$430.21B143.4B361.5D3.4D2.5D35.28B46.3A4.10B$
432.20B143.4B414.29B45.A6.11B$434.21B238.3D2.5D2.3D5.D2.5D4.D3.3D281.
29B52.12B$435.20B237.D3.D.D5.D3.D3.2D4.D5.2D2.D3.D91.2B185.B.29B52.6B
3.4B$434.20B2A236.D5.D9.D2.D.D4.D4.D.D6.D90.3B184.2A31B52.5B4.4B$221.
D3.D.D3.D2.3D3.3D2.5D2.3D3.3D3.3D167.20B2A237.3D2.3D6.D2.D2.D4.D3.D2.
D4.2D90.4B184.2AB.30B52.4B5.4B$221.2D2.D.D3.D.D3.D.D3.D3.D3.D3.D.D3.D
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221.D.D.D.D3.D5.D.D3.D3.D7.D.D2.2D5.D163.A.AB7.11B239.D3.D.D6.D7.D4.D
6.D2.D3.D87.4B192.27B51.2A11.4B$221.D2.2D.D.D.D3.2D3.4D3.D6.D2.D.D.D
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197.26B48.A$221.D3.D.D3.D2.3D3.3D4.D3.5D2.3D3.3D176.A9.4B349.A9.4B
199.26B$440.3A11.4B235.3D2.D3.D8.3D2.5D2.3D4.D74.2A8.4B200.27B$440.A
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456.4B232.D5.D3.D11.D3.D7.D3.D63.A12.5B.4B203.A7.14B2.4B$222.3D2.5D.
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9B7.4B$175.3D2.D3.D2.3D2.5D3.D4.3D2.5D6.D3.D.D9.D3.D4.2D4.2D3.D200.4B
234.D.D.D.D9.D5.D5.D5.D64.2AB.3B3.13B199.A12.5B11.3B$174.D3.D.D3.D.D
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20B2A213.5B10.2B$174.D5.D3.D.D7.D5.D3.D8.D8.3D2.3D5.D5.D5.D5.D3.4D
199.4B229.3D2.D3.D7.5D3.D3.5D2.3D65.20B2A216.2A11.B$175.3D2.D.D.D.4D
4.D5.D3.4D4.D12.D.D6.D6.D5.D5.D3.D3.D536.20B217.A$178.D.D.D.D.D3.D3.D
5.D3.D3.D2.D9.D3.D.D5.D7.D5.D5.D3.D3.D535.21B218.3A$174.D3.D.2D.2D.D
3.D3.D5.D3.D3.D.D11.3D2.5D.D7.D4.3D3.3D3.3D475.4B55.20B223.A$175.3D2.
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4B55.3BCBC4B.7B4.2A$225.4B463.4B36.4B57.2B3C4B2.6B4.A$226.4B463.4B34.
4B57.5BC4B3.6B4.3A$227.4B463.4B32.4B57.10B6.4B6.A$228.4B463.4B30.4B
57.4B12.B2A2B$229.4B463.4B25.B2.4B57.4B14.2A.B2A$230.4B463.4B22.8B57.
4B18.BA.A$231.4B463.4B19.9B57.4B22.A$232.4B9.2A452.4B7.2A9.8B57.4B23.
2A$186.A18.A27.4B6.2B2AB452.B2AB5.B2AB7.8B57.4B$186.3A5.2A7.3A28.4B5.
4B454.BA2B5.3B6.10B55.4B$189.A3.B2AB5.A32.4B4.6B126.D3.D.D3.D2.3D2.5D
3.D4.3D3.3D287.ABAB3.B.B7.9B55.4B$188.2A4.3B5.2A32.4B4.6B125.2D2.D.D
3.D.D3.D3.D4.2D3.D3.D.D3.D287.2A2B.6B6.7B56.3B$188.5B2.B2.2B.3B33.4B.
2B.6B124.D.D.D.D3.D5.D3.D5.D7.D5.D288.10B4.9B9.A$190.14B34.13B124.D2.
2D.D.D.D4.D4.D5.D5.2D5.D281.2A7.24B6.A.A$189.2A14B34.13B123.D3.D.D.D.
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2.D6.D5.D3.D3.D2.D284.A.AB6.22B4.B2A.2A$190.B.2B2A9B29.A.A4.11B123.D
3.D.D3.D.5D3.D4.3D3.3D2.5D282.2AB.3B2.23B2.BA2.A2.A$192.11B32.AB5.10B
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5D222.30B6.2B2AB$179.A4.4B6.6B31.16B148.2BABA2B39.D3.D.D5.D3.D3.D12.D
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B$180.3B4.4B4.6B31.16B147.7B294.2B3C4B2.6B7.7B8.2A$180.4B4.13B32.15B
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182.5BC13B33.13B150.8B2A286.4B12.B2A2B6.8B$183.2B3C13B33.2A12B149.6B.
2B286.4B14.2A.B2A5.8B$182.3BCBC14B32.2A11B149.7B288.4B18.BA.A4.9B$
183.2BC18B31.11B149.8B287.4B22.A6.8B$183.21B32.8B136.B4.2A8.8B286.4B
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3B3.A.AB4.10B283.4B39.A3B$188.17B31.7B137.4B3.2AB.14B64.2B260.3A$187.
19B29.9B137.4B4.17B62.3B261.BA$187.21B28.5BA2B138.4B3.17B50.A10.4B$
187.21B27.5BABA140.5B2.16B.B48.3A7.4B$189.20B27.5B2AB69.3D11.3D54.24B
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26.13B66.D3.D3.3D7.D54.19B3.BA38.A10.9B$189.18B25.16B64.D3.D2.D3.D4.
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5D.5D.5D3.D6.D$189.17B26.17B63.D3.D2.5D6.D53.3BCBC4B.9B44.2AB.3B4.6B
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190.16B26.18B62.D3.D2.D6.D3.D54.2B3C4B2.7B47.7B.7B.BA.A708.D.D.D.D3.D
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5.D5.D3.2D2.D23.D.D6.D6.D5.D3.5D$190.12B25.7BCBC10B135.4B6.11B47.18B
710.D3.D.2D.2D.D3.D3.D5.D5.D4.D4.D3.D19.D3.D.D5.D7.D5.D6.D$191.10B27.
6B3C9B135.4B8.10B45.19B596.3D2.5D.5D.5D2.3D3.3D2.5D75.D3.D.D3.D2.3D3.
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19B.B2A593.D3.D.D5.D7.D3.D3.D.D3.D5.D$195.4B31.16B133.4B8.A2B.8B43.2B
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.D3.D$116.3B6.4B8.2AB71.4B10.5B6.2A18.4B116.A8.12B2.11B40.10B3.4B2A
217.D.D.D.D3.D.D7.D5.D3.D2.2D.D134.D3.D.D3.D2.3D3.3D4.D4.3D3.3D285.D
5.D9.D.D3.D3.D7.D.D2.2D$124.4B10.2B72.4B11.4B5.A20.4B114.2A7.12B3.BAB
.B3.4B38.4B10.2A221.D2.2D.D.D.D.4D4.D5.D3.D.D.D.4D457.3D2.3D6.D3.3D4.
D6.D2.D.D.D$123.4B86.4B9.6B.BA.A21.4B121.10B6.A.A.2A3.4B36.4B12.A221.
D3.D.D.D.D.D3.D3.D5.D3.2D2.D.D3.D35.3D2.D3.D8.3D2.5D2.3D4.D386.D.D7.D
3.D3.D3.D5.D3.2D2.D$122.4B88.4B7.7B.B2A23.4B23.2A94.EA2B.6B4.3A.ABA5.
4B34.4B10.3A222.D3.D.2D.2D.D3.D3.D5.D3.D3.D.D3.D34.D3.D.D3.D7.D3.D3.D
3.D3.D2.2D382.D3.D.D6.D4.D3.D3.D4.D4.D3.D$122.3B90.4B4.11B26.4B22.A
94.EBEB3.B.B5.A3.A4.A4.4B32.4B11.A224.D3.D.D3.D2.3D4.D4.3D3.3D3.3D35.
D5.D3.D11.D3.D7.D3.D383.3D2.5D.5D2.3D4.D3.5D2.3D$216.4B3.11B27.4B18.B
A.A93.BE2B5.3B5.A2.A.4A5.4B30.4B313.3D2.D.D.D.5D4.D4.D6.D4.D$217.17B
28.4B14.2A.B2A4.B88.B2EB5.B2AB6.A.A.A9.4B28.4B317.D.D.D.D9.D5.D5.D5.D
$213.2A3.15B30.4B12.B2A2B5.2B87.4B7.2A8.A3.3A7.4B26.4B314.D3.D.2D.2D
8.D6.D4.D6.D$214.A4.13B32.10B6.4B4.3B86.4B24.A8.3B25.4B316.3D2.D3.D7.
5D3.D3.5D2.3D382.3D2.D3.D2.3D2.5D.5D3.D3.5D2.3D$214.A.AB2.12B2.2A29.
5BC4B3.6B3.4B124.2B25.3B737.D3.D.D3.D.D3.D.D7.D4.2D7.D.D3.D$215.2AB.
15BA.A29.2B3C4B2.6B3.4B409.3B480.D5.D3.D5.D.D7.D5.D6.D2.D3.D$217.16B
3.A28.3BCBC4B.7B2.4B410.4B25.2A453.3D2.D.D.D4.D3.3D4.D5.D5.D4.4D34.3D
2.D3.D3.D4.3D2.5D2.3D2.5D$217.16B3.2A28.2BC19B412.4B24.A457.D.D.D.D3.
D7.D3.D5.D4.D8.D33.D3.D.D3.D2.2D3.D3.D3.D3.D3.D5.D$218.15B33.21B414.
4B20.BA.A453.D3.D.2D.2D2.D4.D3.D3.D5.D3.D9.D33.D5.D3.D3.D3.D2.2D3.D3.
D3.D4.D$217.15B36.18B416.4B16.2B.B2A32.4B38.4B57.4B10.A305.3D2.D3.D.
5D2.3D4.D4.3D2.D6.3D35.3D2.D.D.D3.D3.D.D.D3.D4.4D3.D$215.17B38.16B
417.4B14.5B35.4B36.BA2B59.4B9.3A386.D.D.D.D3.D3.2D2.D3.D7.D2.D$213.
19B39.16B4.2A411.4B13.5B36.4B34.3AB61.4B11.A381.D3.D.2D.2D3.D3.D3.D3.
D7.D.D$213.2BC15B39.17B3.A.A412.4B10.7B37.4B32.A3B63.4B9.2A382.3D2.D
3.D2.3D3.3D4.D4.3D2.D$212.3BCBC4B.7B40.18B2.A415.4B5.12B3.A33.4B30.B
2AB65.4B8.4B300.3D2.D3.D3.D4.3D2.5D3.D4.3D3.3D$213.2B3C4B2.6B41.16B.
3A416.21B.A.A33.4B25.B2.4B67.4B9.B2A298.D3.D.D3.D2.2D3.D3.D3.D4.2D3.D
3.D.D3.D$212.5BC4B3.6B42.12B.BAB2.2A415.5BC15B.A35.4B22.8B69.4B7.BA.A
298.D5.D3.D3.D3.D2.2D3.D5.D3.D2.2D.D3.D$211.10B6.4B43.13B4A2.A415.2B
3C16B37.4B19.9B71.4B6.B2A300.3D2.D.D.D3.D3.D.D.D3.D5.D3.D.D.D2.3D$
210.4B12.B2A2B42.11B.4B.A.2A414.3BCBC16B38.4B7.2A9.8B67.2A4.4B5.3B
303.D.D.D.D3.D3.2D2.D3.D5.D3.2D2.D.D3.D$209.4B14.2A.B2A39.13B2.2A.A
418.2BC15B42.4B5.B2AB7.8B69.A5.4B2.4B300.D3.D.2D.2D3.D3.D3.D3.D5.D3.D
3.D.D3.D$208.4B18.BA.A38.12B4.A.A418.19B42.4B5.3B6.10B68.A.AB3.9B301.
3D2.D3.D2.3D3.3D4.D4.3D3.3D3.3D$207.4B22.A38.12B2.A.A.2A418.20B41.4B
3.B.B7.9B70.2AB.12B.3B373.4B$206.4B23.2A39.10B2.2A423.19B42.4B.6B6.7B
73.16B2A374.4B10.2B$206.3B65.10B427.21B41.10B4.9B9.A63.16BABA74.5D10.
3D282.4B8.2AB$206.2B66.10B426.24B31.2A7.24B6.A.A63.16BAB74.D13.D3.D
282.4B5.BA2BAB4.B$206.B67.9B426.25B32.A8.24B5.A.A62.19B74.D7.3D7.D
283.2BAB4.BA2BA3B.B2A$274.9B425.4B2.20B32.A.AB6.22B4.B2A.2A59.18B2.B
2A72.3D4.D3.D4.2D278.B6.B3A4.B2A6B2A$270.A.2AB.2B.4B424.4B7.14B.B2A
31.2AB.3B2.23B2.BA2.A2.A56.19B3.BA.A71.D6.5D6.D277.2B6.3BA3.7B.2B24.A
$268.3AB2AB4.3B424.4B10.12B.BA.A32.32BABA.A.A.A55.2BC15B7.A71.D6.D6.D
3.D277.3B6.B2AB3.6B25.3A$267.A4.B432.4B10.11B6.A32.33BA.A.A.A55.3BCBC
4B.7B8.2A70.5D3.4D3.3D278.4B6.4B2.5B8.2A15.A$113.D3.D.5D3.D4.3D2.5D8.
3D115.3A.2A372.5D10.3D40.4B12.7B9.2A32.33B.A.A58.2B3C4B2.6B119.D3.D.
5D3.D4.3D2.5D2.3D3.3D218.4B6.11B8.A15.2A$113.2D2.D.D6.2D3.D3.D3.D9.D
3.D116.A.A373.D13.D3.D38.4B15.5B42.29B2.2B.BAB.A56.5BC4B3.5B119.2D2.D
.D6.2D3.D3.D3.D3.D3.D.D3.D218.20B8.A.AB9.5B$113.D.D.D.D7.D3.D3.D3.D
13.D116.A.A373.D7.3D7.D37.4B15.6B40.30B6.2B2AB55.10B5.3B120.D.D.D.D7.
D3.D3.D3.D7.D5.D219.5BC14B8.2AB.3B4.4B$113.D2.2D.3D5.D4.4D3.D3.5D4.D
118.A374.3D4.D3.D4.2D37.4B15.6B39.19B2.12B7.2B55.4B10.7B118.D2.2D.3D
5.D4.3D4.D5.2D5.D221.2B3C13B11.7B.7B$113.D3.D.D7.D7.D3.D11.D494.D6.D
3.D6.D35.4B15.A2.AB41.2BC15B3.11B7.2B55.4B11.2A.B.2A118.D3.D.D7.D3.D
3.D3.D7.D3.D221.3BCBC4B.7B12.16B.B$113.D3.D.D7.D7.D3.D10.D495.D6.D3.D
2.D3.D34.4B16.4AB41.2BCBC4B.7B5.9B7.B2AB53.4B13.A3.A119.D3.D.D7.D3.D
3.D3.D3.D3.D2.D223.2BC15B12.16B2A$113.D3.D.5D2.3D3.3D4.D9.5D492.5D3.
3D4.3D34.4B23.A39.2B3C4B2.6B7.7B8.2A53.4B11.3A5.3A116.D3.D.5D2.3D3.3D
4.D4.3D2.5D220.18B11.15B.B2A$697.4B20.5A38.5BC4B3.6B5.9B61.4B12.A9.A
295.4B80.17B8.18B.B$697.3B21.A41.10B6.4B5.10B59.4B320.4B81.15B.2B2.
20B$697.2B24.A38.4B12.B2A2B6.8B59.4B162.A159.4B81.22BD15B$697.B24.2A
37.4B14.2A.B2A5.8B57.4B162.A.A159.4B80.8B.13BDBD4B.7B$760.4B18.BA.A4.
9B56.3B163.A.A160.4B19.B57.8B3.2B2A9B3D4B2.6B2.B$759.B2AB22.A6.8B219.
3A.2A160.4B14.B2.3B56.2A3.B5.2B2A11BD4B2.6B.B2A$103.2B653.3BA23.2A7.B
2.4B217.A4.B162.2BAB11.9B5.2A49.A10.18B2.9B2A$103.3B651.B3A37.4B217.
3AB2AB161.B3A11.9B4.A47.3A12.B.3B.4B8.8B2.B$103.4B650.BAB39.4B208.2A
8.A.2AB.B160.3BA11.8B.BA.A9.2B36.A19.4B8.10B$104.4B649.2B41.4B208.A
10.6B160.B2AB2.4B3.9B.B2A9.3B55.4B8.4B.6B2A$105.4B648.B43.4B207.A.AB
9.4B161.4B.5B2.11B10.4B54.B2AB8.4B3.5BA.A$106.4B23.2A667.4B207.2AB.3B
4.6B9.2B150.9B2.11B9.4B54.3BA8.4B4.3B4.A$107.4B22.A669.4B208.7B.8B7.
3B151.21B8.4B54.B3A8.4B12.2A$108.4B18.BA.A45.D3.D.D3.D3.D4.3D2.5D3.D
4.3D3.3D579.4B207.17B5.4B152.19B8.4B54.2BAB8.4B$109.4B14.2A.B2A46.2D
2.D.D3.D2.2D3.D3.D3.D4.2D3.D3.D.D3.D579.4B207.15B5.4B151.B2.19B6.4B
66.4B$110.4B12.B2A2B48.D.D.D.D3.D3.D3.D3.D3.D5.D3.D2.2D5.D789.16B4.4B
150.26B3.4B66.4B$111.10B6.4B48.D2.2D.D.D.D3.D4.4D3.D5.D3.D.D.D4.D788.
17B4.4B146.2AB2.27B.4B66.4B$112.5BC4B3.6B48.D3.D.D.D.D3.D7.D3.D5.D3.
2D2.D3.D787.20B2.4B147.3AB2ADB2A21B.4B66.4B$113.2B3C4B2.6B49.D3.D.2D.
2D3.D7.D3.D5.D3.D3.D2.D788.2BC22B148.B2AB3CB2A25B66.4B$112.3BCBC4B.7B
9.2A38.D3.D.D3.D2.3D3.3D4.D4.3D3.3D2.5D784.3BCBC4B.14B149.3ABCAD27B$
113.2BC15B6.2B2AB6.2A861.2B3C4B2.12B150.B2ABD28B$113.19B5.4B7.A861.5B
C4B2.12B153.31B$115.21B.6B2.BA.A860.10B4.12B152.4B2.7B2.16B$117.27B.B
2A860.4B10.12B159.6B3.16B$118.28B861.4B12.9B163.3B5.14B$117.29B860.4B
13.8B165.B4.3B.9B$117.29B859.4B15.6B171.2A3.8B$115.2AB.3B2.22B858.4B
14.7B173.A6.4B$114.A.AB6.13B.9B33.2B821.4B15.2A4.2B169.3A5.4B$114.A8.
12B2.11B32.3B819.4B17.A3.B2AB168.A7.2A$113.2A7.12B3.BAB.B3.2B2A31.4B
817.4B15.3A5.2A178.A$121.10B6.A.A.2A3.BABA31.4B816.3B16.A184.3A$120.
4B.6B4.3A.ABA6.BAB31.4B815.2B202.A$119.4B3.B.B5.A3.A4.A4.B2AB31.4B$
118.4B5.3B5.A2.A.4A5.4B31.4B$117.4B5.B2AB6.A.A.A9.4B31.4B15.2A$117.3B
7.2A8.A3.3A7.4B31.4B13.B2A2B$117.2B24.A8.3B32.4B13.4B$153.2B33.10B5.
5B$154.B34.5BC4B3.6B$190.2B3C4B.8B$189.3BCBC13B7.2A$190.2BC16B6.A$
190.20B2.BA.A$192.19B.B2A$194.19B$195.18B$194.19B$194.19B$192.2AB.3B
2.12B$191.A.AB6.10B.B2A$191.A8.10B2.BA.A$190.2A7.9B7.A$198.10B7.2A$
197.4B.6B$196.4B3.B.B$195.4B5.3B$194.4B5.B2AB$193.4B7.2A$193.3B$193.
2B!
dvgrn
Moderator
 
Posts: 3996
Joined: May 17th, 2009, 11:00 pm
Location: Madison, WI

Re: Glider pair adjustment toolkit

Postby dvgrn » March 14th, 2017, 10:46 pm

Okay, there's an odd detail of glider-pair timing that I ran into recently, that I don't entirely understand yet. Maybe I'll understand it better when I'm done writing this series of posts.

I started out wanting to build a glider-to-LWSS converter, which requires synchronizing two signals:

x = 166, y = 93, rule = LifeHistory
83.2A11.A$83.2A10.A.A$95.A.A2.2A3.A$94.2A.2A2.A2.A.A$98.A.A3.A.A$94.
2A.A2.4A.A3.A9.A$94.2A.A.A3.A5.3A5.3A28.2A$98.A.A3.A7.A3.A13.2A17.A$
99.A.A3.A5.2A3.2A13.A17.A.A$100.A3.2A24.A19.2A$130.2A3$91.2A11.D59.2A
$91.2A9.3D59.2A$76.2A24.D.D$75.A2.A23.D30.2A15.C$74.A.2A55.2A15.C.C$
74.A75.3C$73.2A77.C$88.2A$88.A$89.3A$91.A10.2A$101.A.A11.2A6.A19.2A$
101.A13.2A6.3A18.A$100.2A24.A14.3A$125.2A14.A3$149.C$15.2A11.A120.2C$
15.2A10.A.A118.C.C$27.A.A2.2A3.A$26.2A.2A2.A2.A.A$30.A.A3.A.A$26.2A.A
2.4A.A$26.2A.A.A3.A$30.A.A3.A$31.A.A3.A$32.A3.2A$51.A$49.3A$48.A$23.
2A23.2A$23.2A$8.2A$7.A2.A$6.A.2A$6.A$5.2A$20.2A38.2A$20.A38.A2.A$21.
3A36.2A$23.A11.2A$36.A$33.3A6.A.2A17.2A$33.A6.3A.2A17.A$39.A24.3A$40.
3A.2A20.A$42.A.A$42.A.A4.2A$43.A6.A$2A45.3A$.2A44.A$A5$102.A$100.3A$
99.A$99.2A7$89.2A$88.A.A5.2A$88.A7.2A$87.2A2$101.A$97.2A.A.A$96.A.A.A
.A$93.A2.A.A.A.A.2A$93.4A.2A2.A2.A$97.A4.2A$95.A.A$95.2A!
#C [[ STEP 5 STOP 600 ]]

Notice that with this choice of H-to-2G, the glider is 6 diagonal cells too slow. Another way of looking at it is we need the Herschel to be slower by 24 ticks.

Unfortunately we can't easily use Snarks to adjust this particular geometry by as little as 24 ticks. The smallest delay we can add to a straight-line segment by adding Snarks is 128 ticks, 32 cells diagonally:

x = 91, y = 81, rule = LifeHistory
58.2A$58.A.A$60.A4.2A$56.4A.2A2.A2.A$56.A2.A.A.A.A.2A$58.BABABA.A$.C
26.3BC27.B2ABA.A$2.C26.3BC27.2B.BA$3C27.3CB25.3B$31.4B15.2A6.4B$32.4B
15.A6.B2A3B$33.4B14.A.AB3.B2A4B$34.4B14.2AB.10B$35.4B15.13B$36.4B14.
14B13.A$37.4B10.A2.15B10.3A$38.4B7.3A4.8B2.4B8.A$39.4B5.A7.6B5.4B7.2A
$40.4B4.2A5.9B4.4B3.5B$41.9B4.4B4.2A5.4B2.3B$42.6B5.4B5.A7.9B7.2A$42.
8B2.4B7.3A5.8B8.A$40.15B10.A6.10B3.B.A.2A$40.14B18.7B2A2B.B3A2.A$40.
13B19.7B2A3BAB2.2A$38.2AB.10B20.12B4A$37.A.AB3.B2A4B19.2AB.7B3.2B.A$
37.A6.B2A3B19.A.AB.7B2.B3A$36.2A6.4B14.A6.A5.5B3.A$45.3B14.3A3.2A5.4B
5.5A$46.2B.BA14.A8.4B10.A$45.B2ABA.A.2A9.2A7.4B9.A$44.BABABA.A.A10.5B
3.4B10.2A$42.A2.A.A.A.A.A12.3B2.4B$42.4A.2A2.A.2A.2A7.9B$46.A4.A2.A.A
8.8B$44.A.A3.2A2.A.A.B3.10B$44.2A3.A2.2A2.3AB.2B2A7B$50.2A2.2A2.BA3B
2A7B$52.2A2.4A12B$48.3A2.A2.A.2B3.7B.B2A$47.A3.2A4.3AB2.7B.BA.A$48.A.
A9.A3.5B5.A$49.2A4.5A5.4B5.2A$37.3B15.A10.4B$37.4B16.A9.4B$38.3BD14.
2A10.3BD$39.3BD26.3BD$40.3DB26.3DB$41.4B26.4B$42.2BDB26.4B$43.4B26.3B
$44.2BDB26.2B$45.4B26.B$46.2BDB$47.4B$48.2BDB$49.4B$50.2BDB$51.4B$52.
2BDB$53.4B$54.2BDB$55.4B$56.2BDB$57.4B$58.2BDB$59.4B$60.2BDB$61.4B$
62.2BDB$63.4B$64.2BDB$65.4B$66.2BDB$67.4B$68.2BDB$69.4B$70.3BD$71.3BD
$72.3D!
#C [[ STEP 5 STOP 288 ]]

-- or a bit farther if we want to replace a Snark with a three-Snark loop -- 208 ticks, 52 diagonals:

x = 127, y = 99, rule = LifeHistory
28.2A$27.A.A$21.2A4.A$19.A2.A2.2A.4A$19.2A.A.A.A.A2.A$22.A.A.A.A$22.A
.A.2A$23.A2$36.2A$27.2A7.A$9.A17.2A5.A.A$9.3A22.2A$12.A$11.2A3$3.2A$
3.A$2A.A20.2A18.2A$A2.3A4.2A13.A18.A$.2A3.A3.2A10.3A21.A$3.4A15.A2.3A
14.5A$3.A15.2A.A.A2.A13.A$4.3A12.A.A.2A2.A.A12.3A$7.A13.A6.2A15.A13.
2A$2.5A14.4A17.4A13.A.A$2.A21.A12.2A3.A3.2A13.A4.2A$4.A18.A13.2A4.3A
2.A8.4A.2A2.A2.A$3.2A18.2A20.A.2A8.A2.A.A.A.A.2A$45.A14.A.A.A.A$44.2A
15.2A.A.A$65.A2$36.2A13.2A$36.A15.A7.2A$37.3A12.A.A5.2A$39.A13.2A7$
15.2C16.D21.2C6.2A8.D$14.C.C17.D19.C.C6.A10.D$16.C15.3D21.C7.3A5.3D$
66.A49$125.D$126.D$124.3D!
#C [[ STEP 5 STOP 282 ]]

-- though you can get it as low as 120 ticks, 30 diagonals, if you skip the twist:

x = 171, y = 76, rule = LifeHistory
29.2A$29.A.A$31.A4.2A$27.4A.2A2.A2.A$27.A2.A.A.A.A.2A$30.A.A.A.A$31.
2A.A.A$35.A2$21.2A$22.A7.2A$22.A.A5.2A$23.2A2$52.A62.2A$50.3A62.A.A$
49.A67.A4.2A$49.2A62.4A.2A2.A2.A$113.A2.A.A.A.A.2A$33.2A81.A.A.A.A$
33.A23.2A58.2A.A.A$34.3A21.A62.A$36.A21.A.2A$50.2A4.3A2.A45.2A$50.2A
3.A3.2A47.A7.2A$55.4A49.A.A5.2A$41.2A15.A50.2A$40.A.A12.3A$33.A6.A13.
A$33.3A3.2A14.5A$36.A22.A$35.2A20.A$57.2A$119.2A$27.2A90.A$27.A92.3A$
24.2A.A94.A$24.A2.3A4.2A$25.2A3.A3.2A$27.4A$27.A15.2A$28.3A12.A.A$31.
A13.A$.2C23.5A8.D5.2A54.2C36.D$C.C23.A13.D59.C.C37.D$2.C25.A9.3D61.C
35.3D$27.2A27$169.D$170.D$168.3D!
#C [[ STEP 5 STOP 274 ]]

Any of these can be further slowed by 8N ticks, by moving pairs of Snarks that form a 180-degree turn, outward by N cells diagonally.

Luckily, every Snark turn slows down a glider by 4 ticks. Getting a glider back traveling in the same direction always takes pairs of Snarks, so the effect is that the mod-8 timing of the glider never changes. But we _could_ use the slowdown to solve the particular G-to-LWSS problem that I started with here, just by adding a six-Snark zigzag:

x = 233, y = 122, rule = LifeHistory
150.2A11.A$150.2A10.A.A$162.A.A2.2A3.A$161.2A.2A2.A2.A.A$165.A.A3.A.A
$63.2A26.2A26.2A40.2A.A2.4A.A3.A9.A$63.A.A25.A.A25.A.A39.2A.A.A3.A5.
3A5.3A28.2A$65.A4.2A21.A4.2A21.A4.2A37.A.A3.A7.A3.A13.2A17.A$61.4A.2A
2.A2.A15.4A.2A2.A2.A15.4A.2A2.A2.A36.A.A3.A5.2A3.2A13.A17.A.A$61.A2.A
.A.A.A.2A15.A2.A.A.A.A.2A15.A2.A.A.A.A.2A37.A3.2A24.A19.2A$64.A.A.A.A
21.A.A.A.A21.A.A.A.A70.2A$65.2A.A.A22.2A.A.A22.2A.A.A$69.A27.A27.A$
158.2A71.2A$55.2A26.2A26.2A45.2A71.2A$56.A7.2A18.A7.2A18.A7.2A21.2A$
56.A.A5.2A18.A.A5.2A18.A.A5.2A20.A2.A54.2A15.D$57.2A26.2A26.2A26.A.2A
55.2A15.D.D$11.2A11.A116.A75.3D$11.2A10.A.A114.2A77.D$23.A.A2.2A3.A
50.A27.A42.2A$22.2A.2A2.A2.A.A47.3A25.3A25.4A13.A$26.A.A3.A.A46.A27.A
27.A3.A14.3A$22.2A.A2.4A.A47.2A26.2A26.2A19.A10.2A$22.2A.A.A3.A35.2A
26.2A26.2A43.A.A11.2A6.A19.2A$26.A.A3.A34.A27.A27.A44.A13.2A6.3A18.A$
27.A.A3.A34.3A25.3A25.3A40.2A24.A14.3A$28.A3.2A36.A27.A27.A65.2A14.A$
47.A$45.3A$44.A26.2A26.2A26.2A87.D$19.2A23.2A24.A.A5.2A18.A.A5.2A18.A
.A5.2A80.2D$19.2A49.A7.2A18.A7.2A18.A7.2A79.D.D$4.2A63.2A26.2A26.2A$
3.A2.A$2.A.2A77.A27.A27.A$2.A76.2A.A.A22.2A.A.A22.2A.A.A$.2A75.A.A.A.
A21.A.A.A.A21.A.A.A.A$16.2A38.2A17.A2.A.A.A.A.2A15.A2.A.A.A.A.2A15.A
2.A.A.A.A.2A$16.A38.A2.A16.4A.2A2.A2.A15.4A.2A2.A2.A15.4A.2A2.A2.A$
17.3A36.2A21.A4.2A21.A4.2A21.A4.2A$19.A11.2A44.A.A25.A.A25.A.A$32.A
44.2A26.2A26.2A$29.3A6.A.2A17.2A$29.A6.3A.2A17.A$.2C32.A24.3A$C.C33.
3A.2A20.A$2.C35.A.A$38.A.A4.2A$39.A6.A$43.3A$43.A48$140.A$138.3A$137.
A$137.2A7$127.2A$126.A.A5.2A$126.A7.2A$125.2A2$139.A$135.2A.A.A$134.A
.A.A.A$131.A2.A.A.A.A.2A$131.4A.2A2.A2.A$135.A4.2A$133.A.A$133.2A!
#C [[ STEP 5 STOP 985 ]]

(Out of time for tonight. I'll get to the puzzling problem tomorrow.)
dvgrn
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Re: Glider pair adjustment toolkit

Postby Scorbie » March 15th, 2017, 3:34 am

How about using alternative slower reflectors?
(Including but not only the following:)
viewtopic.php?f=2&t=1599&p=19168&hilit=Scorbie+reflector#p19153
Best wishes to you, Scorbie
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Re: Glider pair adjustment toolkit

Postby dvgrn » March 15th, 2017, 7:40 am

Scorbie wrote:How about using alternative slower reflectors?
(Including but not only the following:)
http://conwaylife.com/forums/viewtopic. ... 168#p19153

Also totally doable. It only takes one 90-degree reflector chosen from simeks' labeled collection to convert any glider to the right color and mod-8 timing to match any required input.

Come to think of it, that collection also allows for alternative hot-swappable A1 and A2 components in chris_c's universal adjustment toolkit. But the best ones I can find offhand are just exactly as wide as the F116-stretched B1 and B2 components that I came up with before:

x = 127, y = 71, rule = LifeHistory
21.3D$21.D$22.D2.B$24.3B$24.4B$25.4B$26.4B$27.4B$28.4B$29.4B67.3D$30.
4B66.D$31.4B66.D2.B$32.4B10.2A55.3B10.2A$33.4B9.A56.4B9.A$34.4B10.A
55.4B10.A$28.2A5.5B4.5A49.2A5.4B5.5A$29.A5.5B3.A55.A5.5B3.A$29.A.AB.
7B2.B3A52.A.AB.7B2.B3A$30.2AB.7B3.2B.A52.2AB.7B3.2B.A$32.12B4A54.12B
4A$32.7B2A3BAB2.2A52.7B2A3BAB2.2A$32.7B2A2B.B3A2.A51.7B2A2B.B3A2.A$
32.10B3.B.A.2A51.10B3.B.A.2A$31.8B8.A53.8B8.A$30.9B7.2A52.9B7.2A$29.
4B2.3B61.4B2.3B$16.2A10.4B3.5B58.4B3.5B$17.A9.4B7.2A45.2A10.4B7.2A$
15.A10.4B8.A47.A9.4B8.A$15.5A5.4B5.2A3.3A42.A10.4B10.3A$20.A3.5B5.A6.
A42.5A5.4B5.2A6.A$17.3AB2.7B.BA.A54.A3.5B5.A$16.A.2B3.7B.B2A52.3AB2.
7B.BA.A$16.4A12B53.A.2B3.7B.B2A$14.2A2.BA3B2A7B53.4A12B$13.A2.3AB.2B
2A7B51.2A2.BA3B2A7B$13.2A.A.B3.10B50.A2.3AB.2B2A7B$16.A8.8B49.2A.A.B
3.10B$16.2A7.9B7.2A42.A8.8B15.2A$26.3B2.4B5.B2AB41.2A7.9B14.A$24.5B3.
4B5.3B51.3B2.4B10.BA.A$24.2A7.4B3.B.B50.5B3.4B2.6B.B2A9.A$25.A8.4B.6B
48.2A7.13B9.3A$22.3A10.10B7.2A40.A8.13B7.A$22.A4.2A7.9B7.A38.3A3.2A5.
11B.5B2.2A$28.A8.10B2.BA.A38.A6.A6.16B.3B$6.C21.A.AB6.10B.B2A24.C21.A
.AB4.17B$7.C10.A10.2AB.3B2.12B27.C10.A10.2AB.3B.17B$5.3CB7.3A12.19B
25.3CB7.3A12.24B$6.4B5.A15.19B26.4B5.A15.23B$7.4B4.2A15.18B27.4B4.2A
15.20B$2A6.9B14.19B20.2A6.9B14.17B.3B$.A7.6B14.19B.B2A19.A7.6B14.18B
3.B$.A.2A5.6B3.B2.2B2.21B2.BA.A18.A.2A5.6B3.B2.2B2.21B$2.A2.A4.36B6.A
19.A2.A4.36B$3.2AB3.36B7.2A19.2AB3.27B.9B$4.14B2A16B.8B29.14B2A16B2.
7B$5.13B2A16B3.6B30.13B2A16B3.5B$6.29B5.5B31.29B5.4B$6.17B.B.2B13.4B
31.17B.B.2B10.4B.B2A$7.15B4.3B11.B2A2B32.15B4.3B9.2A3.BA.A$7.15B5.A2B
.2A8.2A34.15B5.A2B.2A6.A6.A$8.13B5.A.A2B.A45.13B5.A.A2B.A3.3A7.2A$10.
13B2.A.AB2.A48.13B2.A.AB2.A4.A$9.8B4.2A.A.A3.A48.8B4.2A.A.A3.A$9.6B6.
2ABA2.4A.A46.6B6.2ABA2.4A.A$9.5B8.B2.A.A3.A.A45.5B8.B2.A.A3.A.A$9.B.B
9.2A.2A2.A2.A.A45.B.B9.2A.2A2.A2.A.A$10.3B9.A.A2.2A3.A47.3B9.A.A2.2A
3.A$9.B2AB9.A.A54.B2AB9.A.A$10.2A11.A56.2A11.A!

And looking again, I see these new ones are just the old A1 and A2 components with Snarks added to line up the output lanes. I was hoping there would be a pair of 90-degree turners with just one Snark added to each to make hot-swappable 180-degree color preservers -- but I don't see anything particularly compact in simeks' collection.

(On the other hand, that collection was made quite a while ago now -- possibly a fresh survey would turn up something better from the last year's crop of H-to-Gs...)

Anyway, all syringe-based 90-degree turns are a lot bulkier than Snarks. Seems like it may be quite a bit more compact to use a wider range of H-to-2Gs, to produces each glider with exactly the right color and mod-8 phase in the first place, so that only Snarks are needed to get it into its final exact spacetime location.

When I get a chance, I'll try putting together a glider-to-Cordership converter using the above H-to-2G collection -- just see how it comes out. Maybe it won't be as compact as I'm hoping... but I suspect that it will help quite a bit to get rid of all those double-trombone ladder rungs that chris_c's current script produces. EDIT: See here for the first fresh attempt at a glider-to-Cordership V-converter.
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Re: Glider pair adjustment toolkit

Postby dvgrn » March 15th, 2017, 8:32 am

dvgrn wrote:Okay, there's an odd detail of glider-pair timing that I ran into recently, that I don't entirely understand yet...
(Out of time for tonight. I'll get to the puzzling problem tomorrow.)

Okay, here's the odd thing I ran into. Going back to the G-to-H-to-2G-to-LWSS problem above, it's possible to make a good connection by adding two 180-degree trombone slides, one to each signal path -- or to make the H-to-2G be the slidable part:

x = 138, y = 100, rule = LifeHistory
55.2A11.A$54.B2AB9.A.A$55.3B9.A.A2.2A3.A$54.B.B9.2A.2A2.A2.A.A$54.5B
8.B2.A.A3.A.A$54.6B6.2ABA2.4A.A3.A9.A$54.8B4.2A.A.A3.A5.3A5.3A28.2A$
55.13B2.A.AB2.A7.A3.A13.2A17.A$53.13B5.A.A2B.A5.2A.B.2A13.A17.A.AB$
52.15B5.A2B.2A5.7B12.A19.2AB.3B$52.15B4.3B11.3B14.2A20.7B2.2B$51.17B.
B.2B11.6B13.B20.13B$51.29B4.6B2.2B9.3B19.12B$50.13B2A16B2.7B.4B7.6B
16.12B2A$49.14B2A16B2.16B2.10B11.14B2A$48.2AB3.27B.30B3.2B2.18B$47.A
2.A4.50B2A15BD13B$46.A.2A5.6B3.B2.2B2.34B2A15BDBD4B.6B$46.A7.6B14.48B
3D4B2.5B$45.2A6.9B14.48BD4B2.5B$40.2A10.4B4.2A15.51B3.5B$41.A9.4B5.A
15.22B.B3.13B.4B9.6B$39.A10.4B7.3A12.7B2.11B7.7B.B5.3B9.7B$39.5A5.4B
5.3A2.A10.2AB.3B6.4B.3B20.4B9.8B$44.A4.4B5.A2.A11.A.AB9.B2A2B4.A19.2A
10.9B$41.3AB2.7B.BA.A2.2A10.A13.2A6.3A18.A9.4B.5B$40.A.2B3.7B.B2A14.
2A24.A14.3A9.4B2.5B$40.4A12B41.2A14.A10.4B3.5B$38.2A2.BA3B2A7B67.4B4.
5B$37.A2.3AB.2B2A7B66.4B5.5B$37.2A.A.B3.10B65.D3B6.5B$40.A8.8B63.B2DB
7.5B$40.2A7.9B61.BDBD8.5B$50.3B2.4B59.4B9.5B$48.5B3.4B57.4B10.5B$48.
2A7.4B55.4B11.5B$49.A8.4B53.4B12.5B$46.3A10.4B10.2A39.4B13.5B$46.A13.
4B9.A39.4B14.5B$61.4B10.A36.4B15.5B$55.2A5.4B5.5A35.4B16.5B$11.2A11.A
31.A5.4B4.A39.4B17.5B$10.B2AB9.A.A30.A.AB.7B2.B3A35.4B18.5B$11.3B9.A.
A2.2A3.A9.4D10.2AB.7B3.2B.A33.4B19.5B$10.B.B9.2A.2A2.A2.A.A8.2D14.12B
4A32.4B20.5B$10.5B8.B2.A.A3.A.A8.D.D13.7B2A3BAB2.2A29.4B21.5B$10.6B6.
2ABA2.4A.A9.D2.D12.7B2A2B.B3A2.A27.4B22.5B$10.8B4.2A.A.A3.A15.D11.10B
3.B.A.2A26.4B23.5B$11.13B2.A.AB2.A15.D9.8B8.A28.4B24.5B$9.13B5.A.A2B.
A15.D7.9B7.2A27.4B25.5B$8.15B5.A2B.2A16.D5.4B2.3B36.4B26.5B$8.15B4.3B
17.A7.4B3.5B21.2A10.4B27.5B$7.17B.B.2B16.3A6.4B7.2A22.A9.4B28.5B$7.
29B8.A8.4B.2B5.A21.A10.4B29.5B$6.13B2A16B7.2A6.10B4.3A18.5A5.4B5.2A
23.5B$5.14B2A16B2.B.5B5.4B.7B5.A23.A4.4B5.A24.5B$4.2AB3.27B.6B6.4B.9B
25.3AB2.7B.BA.A24.5B$3.A2.A4.34B4.4B3.9B23.A.2B3.7B.B2A25.5B$2.A.2A5.
6B3.B2.2B2.25B4.10B22.4A12B27.5B$2.A7.6B14.21B4.12B19.2A2.BA3B2A7B27.
5B$.2A6.9B14.19B3.9B.4B17.A2.3AB.2B2A7B27.5B$8.4B4.2A15.23B2A3B4.4B
16.2A.A.B3.10B$7.4B5.A16.22BA2BA2B5.4B18.A8.8B$6.4B7.3A11.8B2.15B2A2B
7.4B17.2A7.9B$5.4B10.A11.2A3.B5.17B9.4B26.3B2.4B$4.4B24.A7.21B8.4B23.
5B3.4B10.2A$3.4B22.3A6.A.2AB2.6B.2B5.2A9.4B22.2A7.4B9.A$2.4B23.A6.3AB
2AB2.6B8.A11.4B22.A8.4B10.A$.A3B30.A4.B5.5B9.3A2.D6.4B18.3A3.2A5.4B5.
5A$B2AB32.3A.2A5.4B11.A3.D6.4B17.A6.A5.4B4.A$ABA35.A.A4.5B17.D6.4B23.
A.AB.7B2.B3A$38.A.A4.2A21.D6.4B23.2AB.7B3.2B.A$39.A6.A22.D2.D3.4B24.
12B4A$43.3A24.D.D4.4B23.7B2A3BAB2.2A$43.A27.2D5.4B22.7B2A2B.B3A2.A$
69.4D6.4B21.10B3.B.A.2A$80.4B19.8B8.A$81.4B10.A6.9B7.2A$82.4B7.3A5.4B
2.3B$83.4B5.A7.4B3.5B$84.4B4.2A5.4B7.2A$85.9B4.4B8.A$86.6B5.4B10.3A$
86.8B2.4B13.A$84.15B$84.14B$84.13B$82.2AB.10B$81.A.AB3.B2A3B$81.A6.B
2A3B$80.2A6.4B$89.3B$90.2B.BA$89.B2ABA.A$88.BABABA.A$86.A2.A.A.A.A.2A
$86.4A.2A2.A2.A$90.A4.2A$88.A.A$88.2A!
#C [[ STEP 5 ]]

That's still five Snarks, though. So I tried changing the H-to-2G orientation to see if that would tighten things up:

x = 135, y = 128, rule = LifeHistory
22.A$13.A.A6.3A$14.2AB8.A$14.A3B6.A.A$15.4B5.A.AB$16.4B5.A3B$17.4B6.
4B$18.4B5.6B$19.4B4.7B$20.4B2.8B.4B.B$21.17B.B2A$22.18B2A$22.16B.2B$
22.16B$22.15B$20.2AB.12B$19.A.AB2.11B$19.A5.10B$18.2A5.2B2A6B17.2A11.
A$24.3B2A6B16.B2AB9.A.A$25.10B17.3B9.A.A2.2A3.A$25.8B.B2A.A12.B.B9.2A
.2A2.A2.A.A$24.7B3.B2AB3A10.5B8.B2.A.A3.A.A$24.6B6.B4.A9.6B6.2ABA2.4A
.A3.A9.A$25.6B4.2A.3A10.8B4.2A.A.A3.A5.3A5.3A28.2A$25.5B4.A2.2A13.13B
2.A.AB2.A7.A3.A13.2A17.A$24.8B.A.A14.13B5.A.A2B.A5.2A.B.2A13.A17.A.AB
$24.8BA.A.2A.A9.15B5.A2B.2A5.7B12.A19.2AB.3B$15.2A7.6B.2BAB.A.2A9.15B
4.3B11.3B14.2A20.7B2.2B$16.A6.7B2.2B2.A11.17B.B.2B11.6B13.B20.13B$16.
A.AB3.7B3.B.2A11.29B4.6B2.2B9.3B19.12B$17.2AB2.8B2.A.A2.2A8.13B2A16B
2.7B.4B7.6B16.12B2A$19.11B2.2A2.A2.A6.14B2A16B2.16B2.10B11.14B2A$19.
11B7.2A6.2AB3.27B.30B3.2B2.18B$14.A4.11B14.A2.A4.50B2A15BD13B$13.A.A
2.11B14.A.2A5.6B3.B2.2B2.34B2A15BDBD4B.6B$13.A.A3.7B17.A7.6B14.48B3D
4B2.5B$11.3A.2A2.8B15.2A6.9B14.48BD4B2.5B$10.A4.B4.8B9.2A10.4B4.2A15.
51B3.5B$11.3AB2AB2.7B11.A9.4B5.A15.22B.B3.13B.4B9.6B$13.A.2AB.9B8.A
10.4B7.3A12.7B2.11B7.7B.B5.3B9.7B$15.13B8.5A5.4B5.3A2.A10.2AB.3B6.4B.
3B20.4B9.8B$8.2A7.11B13.A4.4B5.A2.A11.A.AB9.B2A2B4.A19.2A10.9B$9.A7.
9B.B2A8.3AB2.7B.BA.A2.2A10.A13.2A6.3A18.A9.4B.5B$9.A.AB2.10B2.BA.A6.A
.2B3.7B.B2A14.2A24.A14.3A9.4B2.5B$10.2AB.11B5.A6.4A12B41.2A14.A10.4B
3.5B$12.13B5.2A3.2A2.BA3B2A7B67.4B4.5B$12.13B9.A2.3AB.2B2A7B66.4B5.5B
$12.14B8.2A.A.B3.10B65.D3B6.5B$13.14B10.A8.8B63.B2DB7.5B$17.5B2.4B9.
2A7.9B61.BDBD8.5B$16.6B3.4B18.3B2.4B59.4B9.5B$16.6B4.4B15.5B3.4B57.4B
10.5B$17.6B4.4B14.2A7.4B55.4B11.5B$17.3BA3B2.B.4B14.A8.4B53.4B12.5B$
17.2BABA11B10.3A10.4B51.4B13.5B$17.2BABA7B.4B9.A13.4B49.4B14.5B$17.3B
A9B.4B23.4B47.4B15.5B$15.2AB.11B2.4B23.4B45.4B16.5B$14.A.AB2.9B4.4B
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4B10.A28.4B19.5B$9.A13.4B9.4B16.2A5.4B5.5A27.4B20.5B$9.3A10.4B11.4B
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4B15.4B15.2AB.7B3.2B.A25.4B23.5B$11.5B3.4B17.4B16.12B4A24.4B24.5B$13.
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2.A19.4B26.5B$3.A8.8B23.4B5.A7.10B3.B.A.2A18.4B27.5B$2A.A.B3.10B25.4B
4.2A5.8B8.A20.4B28.5B$A2.3AB.2B2A7B26.9B4.9B7.2A19.4B29.5B$.2A2.BA3B
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22.13B10.3A20.4B34.5B$2.5A5.4B5.2A19.2AB.10B13.A19.4B35.5B$2.A10.4B
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34.4B$16.4B29.3B33.4B$17.4B29.2B.BA29.4B$18.4B27.B2ABA.A27.4B$19.4B
25.BABABA.A26.4B$20.4B22.A2.A.A.A.A.2A22.4B$21.4B21.4A.2A2.A2.A21.4B$
22.4B24.A4.2A22.4B$23.4B21.A.A27.4B$24.4B20.2A27.4B$25.4B47.4B$26.4B
45.4B$27.4B43.4B$28.4B41.4B$29.4B39.4B$30.4B37.4B$31.4B35.4B$32.4B33.
4B$33.4B31.4B$34.4B29.4B$35.4B27.4B$36.4B25.4B$37.4B23.4B$38.4B21.4B$
39.4B19.4B$40.4B10.A6.4B$41.4B7.3A5.4B$42.4B5.A7.4B$43.4B4.2A5.4B$44.
9B4.4B$45.6B5.4B$45.8B2.4B$43.15B$43.14B$43.13B$41.2AB.10B$40.A.AB3.B
2A3B$40.A6.B2A3B$39.2A6.4B$48.3B$49.2B.BA$48.B2ABA.A$47.BABABA.A$45.A
2.A.A.A.A.2A$45.4A.2A2.A2.A$49.A4.2A$47.A.A$47.2A!
#C [[ STEP 5 STOP 750 ]]

After the 90-degree turn, it's no longer possible to get the two signals lined up correctly by adjusting Snarks. I didn't expect that.

My current theory is that this only happens if the two output gliders are different colors -- the signal paths must end up being different lengths by a half diagonal after the rotation, for some reason that I'm not quite clear on yet.

Presumably another 90-degree rotation would cause another 4-tick adjustment and put the signals back in 0-mod-8 alignment.
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Re: Glider pair adjustment toolkit

Postby dvgrn » May 1st, 2017, 10:03 am

dvgrn wrote:Okay, here's the odd thing I ran into... I tried changing the H-to-2G orientation to see if that would tighten things up:
...
After the 90-degree turn, it's no longer possible to get the two signals lined up correctly by adjusting Snarks. I didn't expect that.

My current theory is that this only happens if the two output gliders are different colors -- the signal paths must end up being different lengths by a half diagonal after the rotation.

That seems to be correct. There's an update now in the post at the top of this page, with a little more detail on how the different equivalence classes of glider pairs behave when the H-to-2G is rotated or reflected. The four classes Oo1, Ee1, Oe3, Eo3 change into each other after any rotation or reflection, whereas two classes don't change at all, and the others only change half the time so there's only one other "related" class.

The strange behavior of Oo1/Ee1/Oe3/Eo3 makes sense, because the gliders are out of step with each other, so the bounding box changes size in one direction or another with every tick. Very likely there's a less confusing mathematical description of these sixteen classes -- maybe the [same-color/opposite-color, relative phase 0 through 7] that I mentioned. That might be easier for a script to understand, but I think it's a lot harder for a human to calculate manually. So I'm going to stick with the [E|O][e|o][0..3] classes.

Along those lines, there's a new script in town, also in the first post at the top of this thread. Now you can select any two gliders, not just ones in the canonical directions NW and SE, and it will figure out what the equivalent NW and SE gliders would be and tell you what kind of H-to-2G can build those gliders.

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

I think the next task along these lines is to come up with a similarly standardized rating for H-to-3G, H-to-4G, etc., converters. Another improvement in efficiency will be possible for N-glider synchronization circuitry, when it's possible to find a compact G-to-{N}G where the N output gliders are all in the right relative phases. Right now we probably block off a third glider output sometimes from an H-to-2Gs, and add another whole new H-to-2G to generate another synchronized glider, when the third suppressed glider would have worked perfectly well.

A comprehensive toolkit of the 16C2 = 120 H-to-3G equivalence classes seems within reach, and even a collection of the 16C3 = 560 different H-to-4G classes seems technically possible. Maybe not really very useful, though. With three or four outputs, the order and timing of the outputs starts making more of a difference, so it would be necessary to collect several examples of each class to be more likely to have one that solves a given circuit problem.

Anyway, if anyone wants to give the new script a try and report any bugs, I'd be most grateful. Happy circuit-building --
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Re: Glider pair adjustment toolkit

Postby Goldtiger997 » October 13th, 2017, 9:10 am

dvgrn wrote:Maybe post your updated stamp collection to the glider-pair adjustment toolkit thread, when you get a chance? Every little bit helps.


Sorry, I forgot about this. Here is the stamp collection with the H-to-2Gs from range 19-25 added:

glider splitters2.rle
It wouldn't fit in a post
(86.63 KiB) Downloaded 10 times

There was still a bit of re-organisation left to do after using it on the glider-to-adjustable cordership converter. I am not sure if I did the multiple classing correctly, but it's workable for me anyway.

Sorry kind of offtopic below:
dvgrn wrote:
gmc_nxtman wrote:It's also good to know that a copperhead v-gun can be made if necessary - 200 seems like a good period.

I've given up the gun-building business -- but a V-shaped glider-to-copperhead converter certainly might happen at some point. (And then anyone is welcome to attach a p200 gun, of course.)


I was thinking of puting the improved copperhead synthesis on my to-make-a-stable-converter-of-at-some-point-list, but the above comment confused me. I don't really understand why in this case a V shape is better, since it doesn't give any edgy properties like the V gun.
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