Some statistics for 8-cell noncompact methuselahs

[Tropylium]

I've just finish'd a runthru of all the possible pi+block/blinker collisions (about 1500; I did not record the exact number), taking note of any that run over 2000 generations (of which there were 137) or produce something interesting.

The two longest-lived go well-over 7000 generations.

For starters, here's a lame-ass ASCII histogram of the distribution of lifespans, in increments of 100:
2000+ ||||||||||||||
2100+ ||||||||||||
2200+ ||||||||||||||||
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4000+ ||||
4100+ ||
4200+
4300+ |
4400+ |
4500+ |||||
4600+ |
4700+ ||
4800+ |
4900+ ||
5000+
5100+
5200+
5300+
5400+ |
5500+ ||
5600+ |
5700+
5800+
5900+ |
6000+
6100+ |
6200+
6300+
6400+
6500+
6600+
6700+
6800+
6900+
7000+
7100+
7200+
7300+
7400+ |
7500+
7600+
7700+
7800+
7900+ |

(This includes some degenerate cases, where differently placed blonks cause identical perturbations.)

Full dataset included for those interested (but more details of analysis coming in further posts).

[Tropylium]

Objects Observed

Aside from thousands of blocks and blinkers, hundreds of shipties and longboats, dozens of mangos and beacons, etc, here are the less trivial objects that turn'd up. Temporary items (that did not survive to the final census) are mark'd by a dagger (†) here; I do not garantee having caught all such cases, having relied on nothing more than a standard-issue visual cortex for detection. (The data files have some of the barges and mangos noted too, but they were just a bit too abundant that I got bored of keeping track of every instance.)
LWSS: 12+4†
Eater: 1+16†
Long barge: 4+7†
Pulsar: 3+5†
Integral: 2+5†
Aircraft carrier: 2+3†
Bipond: 2+2†
Long ship: 2+2†
Big S: 1+3†
Long eater: 1+2† [aka shillelagh, see my topic "Naming patterns"]
Snake: 1+2†
Very long boat: 1+1†
Tub with tail: 1
2×boattie: 1
Canoe: 1
Pentadecathlon: 1 (I see this particular pattern was reported in the accidental discoveries thred a while ago, too.)
Tub with long tail: 1†
Hat: 1†
Long integral: 1†
Loop: 1†
Boat with tail: 1†
Paperclip: 1†
Bookends: 1†
MWSS: 1†
Table on table: 1†

The fastest LWSS-producing reaction does not even produce any gliders:

Code: Select all

x = 6, y = 20, rule = life
5bo$5bo$5bo15$bo$3o$obo!

This reaction that yields an integral, a blinker and a B is fairly clean as well:

Code: Select all

x = 13, y = 3, rule = life
bo9b2o$3o9bo$obo!

(Also: any idea why eaters are doing that crappy a job at surviving? They're doing worse than the renown'dly humungous pulsars, FFS.)

[Tropylium]

Viable Reactions

I'm still sorting these out (no miraculous transparent junk reactions caught, at least), but here's one amusing but probably almost useless discovery. One of the reactions with a block leaves the block intact, yielding after 264 ticks and a lot of smoke a glider and another block… and it turns out the block is located so that with the addition of another block, an incoming glider can turn it into a pi, and near repeat of the reaction. I say "near", because the apparatus ends up mirror'd in the process! The output glider, too, is merely path-shifted, not reflected in any way. But amusing all the same…

Code: Select all

x = 76, y = 78, rule = life
60bo$61bo$59b3o4$74b2o$74b2o5$67b2o5b2o$67b2o5b2o62$bo$b2o$obo!

[skomick]

Viable Reactions
...here's one amusing but probably almost useless discovery. One of the reactions with a block leaves the block intact, yielding after 264 ticks and a lot of smoke a glider and another block… and it turns out the block is located so that with the addition of another block, an incoming glider can turn it into a pi, and near repeat of the reaction. I say "near", because the apparatus ends up mirror'd in the process! The output glider, too, is merely path-shifted, not reflected in any way. But amusing all the same…

Code: Select all

x = 76, y = 78, rule = life
60bo$61bo$59b3o4$74b2o$74b2o5$67b2o5b2o$67b2o5b2o62$bo$b2o$obo!

This reaction (found by Paul Callahan in July '94) was made into an interesting oscillator with period 936.

Code: Select all

x = 120, y = 134, rule = B3/S23
29b3o$32bo55b2o$28bo3bo55b2obo$18bo8bobo2bo59bo8bo$18b3o4bo2bobo58bo9b
3o$21bo3bo3bo60bob2o4bo$20b2o3bo66b2o4b2o$26b3o$23bo72bo$22bobo70bobo$
18b2o2b2o72b2o2b2o$18b2o80b2o2$2bo114bo$b3o$3obo110b3obo$bo3bo108bob2o
$2bo3bo107b2obo$3bob3o104bob3o$4b3o$5bo108bo$9bo100bo$8bobo98bobo$9b2o
98b2o$5b2o106b2o$4bobo106bobo$4bo5b2o96b2o5bo$3b2o5b2o96b2o5b2o36$36b
2o5b2o30b2o5b2o$36b2o5b2o30b2o5b2o2$44bo$43b2o$43bobo$36b2o44b2o$36b2o
44b2o35$36bo$3b2o5b2o24b2o70b2o5b2o$4bo5b2o23bobo70b2o5bo$4bobo106bobo
$5b2o106b2o$9b2o98b2o$8bobo98bobo$9bo100bo$5bo108bo$4b3o$3bob3o104bob
3o$2bo3bo107b2obo$bo3bo108bob2o$3obo110b3obo$b3o$2bo114bo2$18b2o80b2o$
18b2o2b2o72b2o2b2o$22bobo70bobo$23bo72bo$26b3o$20b2o3bo66b2o4b2o$21bo
3bo3bo60bob2o4bo$18b3o4bo2bobo58bo9b3o$18bo8bobo2bo59bo8bo$28bo3bo55b
2obo$32bo55b2o$29b3o!

[knightlife]

I like your implied separation of methuselahs into two groups: compact and non-compact. This is an excellent distinction when trying to define "methuselah" (see the other thread about defining methuselahs).

BTW, these are 9-cell patterns, just sayin'

[Tropylium]

I like your implied separation of methuselahs into two groups: compact and non-compact. This is an excellent distinction when trying to define "methuselah" (see the other thread about defining methuselahs).

Yes, that is one issue I'm hoping to clarify here. Another is what qualifies as an "exceptional" lifespan.

Thie distinction itself is a bit hairy too, however. Take bunnies, for example: its two halves develop independantly for 2 ticks (bunnies 9 for 25 ticks, etc.) Does this count for anything? Or what about the fact that 7468M splits fairly quickly into a pi + beehive reaction? Most (but not all — the B-heptomino, for example) methuselahs become more or less "noncompact" at some point anyway, functioning on a principle of "cloud-of-activity runs into debris, which keeps it running longer than it otherwise would have".

BTW, these are 9-cell patterns, just sayin'

Yup. The choice between the two 5-cell pi ancestors is arbitrary in almost all cases, so I started right away from the A-hexomino stage (which I've always view'd as the "real" parent of the pi sequence, BTW; it's the smallest ancestor with the full symmetry, whereas the pi stage itself seems to carry no special significance). The same argument can be applied to the choice of preblock as well…

[david_spencer]

Cool stuff! I'd played around with this a bit before, but I'd never tried enumerating all of the possibilities. Makes me want to try a script myself...

OK, here are the longest-lasting collisions of Acorn and blinkers (I also tried pre-blocks but those collisions were not as fruitful).

22713 generations:

Code: Select all

x = 107, y = 92, rule = B3/S23
$bo$bo$bo85$100bo$102bo$99b2o2b3o!

20636 generations:

Code: Select all

x = 85, y = 94, rule = B3/S23
$b3o89$78bo$80bo$77b2o2b3o!

18669 generations:

Code: Select all

x = 55, y = 108, rule = B3/S23
$b3o103$48bo$50bo$47b2o2b3o!

As you can see, most of the time the extra object is way in the upper left, which makes sense because the chaos takes a long time to reach there. Here is the most notable exception.

16845 generations:

Code: Select all

x = 40, y = 52, rule = B3/S23
$36b3o47$2bo$4bo$b2o2b3o!

That pattern is also the smallest bounding box to pass 15000, although two patterns that passed 14500 have smaller bounding boxes, like

14628 generations:

Code: Select all

x = 23, y = 49, rule = B3/S23
$21bo$21bo$21bo42$2bo$4bo$b2o2b3o!

I also tried crashing Acorn into object with four-cell predecessors. I found four that went past 17000:

21552 generations:

Code: Select all

x = 29, y = 44, rule = B3/S23
$24b4o39$2bo$4bo$b2o2b3o!

19681 generations:

Code: Select all

x = 84, y = 119, rule = B3/S23
$bo$bo$bo$bo111$77bo$79bo$76b2o2b3o!

17229 generations:

Code: Select all

x = 72, y = 42, rule = B3/S23
$65bo$67bo$64b2o2b3o34$bo$bo$bo$bo!

17115 generations:

Code: Select all

x = 50, y = 77, rule = B3/S23
$bo$bo$bo$bo69$43bo$45bo$42b2o2b3o!

Smallest bounding box, at 15553 generations:

Code: Select all

x = 52, y = 5, rule = B3/S23
$2bo46bo$4bo43b3o$b2o2b3o!

Maybe later I'll try colliding R-pentominos or something.

[Tropylium]

Are these acorn collisions from a random selection or are you going for some degree of completeness?

What makes enumerating all effectivly different collisions with larger methuselahs like this much more of a pain is the "glider-blinker mess" reaction (and similar ones with larger objects):

Code: Select all

x = 5, y = 6, rule = B3/S23
4bo$4bo$4bo$3o$2bo$bo!

This puts out one glider back towards the parent methuselah, which may be timed in all kinds of ways by placing the blinker farther away; possibly leading to different final outcomes if the parent is still going by the time.

The issue gets even hairier if a methuselah puts out gliders sufficiently close to each other. With this even otherwise "flightless" reactions between a glider and an object (say, g+block > pi) may end up emitting back-gliders.

—And yes, I also noted that collisions with blocks are less likely to yield extended lifespan than collisions with blinkers. Should not be a huge surprize given the block's eater capabilities.