## Challenges

A forum where anything goes. Introduce yourselves to other members of the forums, discuss how your name evolves when written out in the Game of Life, or just tell us how you found it. This is the forum for "non-academic" content.

### Re: Challenges

is a c/1 knightship possible?
`x = 8, y = 10, rule = B3/S233b2o\$3b2o\$2b3o\$4bobo\$2obobobo\$3bo2bo\$2bobo2bo\$2bo4bo\$2bo4bo\$2bo!`

No football of any dui mauris said that.

83bismuth38

Posts: 453
Joined: March 2nd, 2017, 4:23 pm
Location: Still sitting around in Sagittarius A...

### Re: Challenges

83bismuth38 wrote:is a c/1 knightship possible?

`x = 11, y = 19, rule = R5,C4,M0,S83..98,B10..108,NN:T1000,1000\$4.C\$5.CB\$5.2CBA\$5.2C2BA\$5.2C2B2A\$5.2C2B2A\$5.2C2B2A\$5.2C2B2A\$4.3C2B2A\$4.2C3B2A\$3.3C2B3A\$2.3C3B2A\$.3C3B3A\$2.C3B3A\$4.B3A\$6.A!`
If you're the person that uploaded to Sakagolue illegally, please PM me.
`x = 17, y = 10, rule = B3/S23b2ob2obo5b2o\$11b4obo\$2bob3o2bo2b3o\$bo3b2o4b2o\$o2bo2bob2o3b4o\$bob2obo5bo2b2o\$2b2o4bobo2b3o\$bo3b5ob2obobo\$2bo5bob2o\$4bob2o2bobobo!`

(Check gen 2)

Saka

Posts: 3018
Joined: June 19th, 2015, 8:50 pm
Location: In the kingdom of Sultan Hamengkubuwono X

### Re: Challenges

p1 puffer
One big dirty Oro. Yeeeeeeeeee...

gameoflifemaniac

Posts: 752
Joined: January 22nd, 2017, 11:17 am
Location: There too

### Re: Challenges

gameoflifemaniac wrote:p1 puffer

`x = 8, y = 8, rule = B2ace5-er/S2ae3aeir4q5i4bo\$3b2obo\$bo4b2o\$ob3obo\$ob3obo\$bo4b2o\$3b2obo\$4bo!`
This post was brought to you by the letter D, for dishes that Andrew J. Wade won't do. (Also Daniel, which happens to be me.)
Current rule interest: B2ce3-ir4a5y/S2-c3-y

drc

Posts: 1664
Joined: December 3rd, 2015, 4:11 pm
Location: creating useless things in OCA

### Re: Challenges

Possible isotropic rule example for Golly 3.0: find a 16x16 soup in B2-a5/S1e2-a35678 -- a distant Just Friends relative -- that displays the most different kinds of reactions before stabilizing inside a finite bounding box.

Here's my first candidate --
`x = 16, y = 16, rule = B2-a5/S1e2-a356782bobobob4obobo\$bob2obo2bo2b2o\$2bobo4b3ob3o\$3obo5bob2o\$3o4b2o4b3o\$2o5b8o\$bo2bo5b3o\$o2b2o4bo2b2o\$o2bobob3o4bo\$2o2b4o3b3o\$3o2b2obo3b4o\$3bo5bob2ob2o\$o4b6o2b2o\$4ob3obob2o\$2b4ob2o3bobo\$ob2o4b4ob2o!`

-- but I don't like it all that much. It starts out well, but then it turns out that its huge final population is all due to one trick at the end.

Here's the script that found it. Hit 'q' to stop searching and display the soup with the highest population found so far:

`from __future__ import divisionimport golly as gbest=0bestpat = []count=0while 1:  g.new(str(count)+": "+str(best))  g.select([0,0,16,16])  g.randfill(50)  clist = g.getcells(g.getselrect())  g.run(16384)  r = g.getrect()  if r==[]: r=[0,0,1,1]  g.run(4096)  r2 = g.getrect()  if r2==[]: r2=[0,0,1,1]  if r2[2]>r[2] or r2[3]>r[3]:    continue # if 1000*int(g.getpop())/r[2]/r[3]+r[2]+r[3]>best:  if int(g.getpop())>best:    best = int(g.getpop())    bestpat = clist[:]  count+=1  g.fit()  g.update()  k = g.getevent()  if k=="key q none":    g.new("Best")    g.putcells(bestpat)    g.exit()`

I tried a couple other metrics, like highest density and largest bounding box, and different run times -- presumably this script will throw away occasional methuselahs with >16384 run times, which would be great candidates for the challenge. But the search gets a lot slower if you bump that number up too high.

dvgrn
Moderator

Posts: 5718
Joined: May 17th, 2009, 11:00 pm

### Re: Challenges

Challenge: Find a garden of eden in B8/S012345678, in which these two patterns are mapped to the same configuration:
`x = 8, y = 3, rule = B8/S0123456783o2b3o\$obo2b3o\$3o2b3o!`
This post was brought to you by the letter D, for dishes that Andrew J. Wade won't do. (Also Daniel, which happens to be me.)
Current rule interest: B2ce3-ir4a5y/S2-c3-y

drc

Posts: 1664
Joined: December 3rd, 2015, 4:11 pm
Location: creating useless things in OCA

### Re: Challenges

drc wrote:Challenge: Find a garden of eden in B8/S012345678, in which these two patterns are mapped to the same configuration:
`x = 8, y = 3, rule = B8/S0123456783o2b3o\$obo2b3o\$3o2b3o!`

Done:

`x = 3, y = 3, rule = B8/S0123456783o\$obo\$3o!`

A more fun solution, which works for *any* rule with two 3-by-3 configurations P and Q mapping to the same configuration, is as follows:

• Consider a pattern of size (5n - 2) by (5n - 2). If it occurs within generation 1 of a pattern, then that 'father' can be assumed to be 5n by 5n. (We take 'father' more liberally to allow junk outside the target 'child'.)
• Suppose the father exists. Divide it into n^2 5-by-5 regions. If any of them is P with an empty border, replace it with Q with an empty border.
• This means there are only (2^25 - 1) ^ (n^2) putative fathers worth considering.
• However, there are 2^((5n-2)^2) patterns of size (5n - 2) by (5n - 2). Whenever n >= 232581596, this is greater than the previous value.
• Hence there exists a GoE of size 1162907980 by 1162907980.
• An explicit GoE is therefore obtained by tiling together all possible patterns of this size, in lexicographical order, into an immense square. The resulting pattern is a colossal square of side-length 1162907980 * 2 ^ 676177484973840200.
What do you do with ill crystallographers? Take them to the mono-clinic!

calcyman

Posts: 2060
Joined: June 1st, 2009, 4:32 pm

### Re: Challenges

Alright, does this count for B8/S01234567?:
`x = 10, y = 3, rule = B8/S012345674o2b4o\$o2bo2b4o\$4o2b4o!`

I'm trying to find a rule that's REALLY difficult to find a GoE for.
This post was brought to you by the letter D, for dishes that Andrew J. Wade won't do. (Also Daniel, which happens to be me.)
Current rule interest: B2ce3-ir4a5y/S2-c3-y

drc

Posts: 1664
Joined: December 3rd, 2015, 4:11 pm
Location: creating useless things in OCA

### Re: Challenges

drc wrote:I'm trying to find a rule that's REALLY difficult to find a GoE for.

B13578/S02468 should be excruciatingly difficult. Without the B8, this is the Fredkin replicator rule (which is reversible ergo has no GoEs), but the B8 makes it irreversible. In particular, the following two patterns have the same descendant:

`x = 129, y = 29, rule = B13578/S0246811o7b11o71b11o7b11o\$11o7b11o71b11o7b11o\$11o7b11o71b11o7b11o\$3ob3ob3o7b3ob3ob3o71b3ob3ob3o7b3ob3ob3o\$4o2bobo3b2ob2o3bobo2b4o71b11o7b11o\$4o2bobo3b2ob2o3bobo2b4o71b11o7b11o\$11o7b11o71b11o7b11o\$3o3b3o3b2ob2o3b3o3b3o71b3ob3ob3o7b3ob3ob3o\$11o7b11o71b11o7b11o\$4o2bobo3b2ob2o3bobo2b4o71b11o7b11o\$4o2bobo3b2ob2o3bobo2b4o71b11o7b11o2\$4b2obob2ob2ob2ob2obob2o\$4b2obob2ob2ob2ob2obob2o2\$4b2obob2ob2ob2ob2obob2o\$4b2obob2ob2ob2ob2obob2o2\$4o2bobo3b2ob2o3bobo2b4o71b11o7b11o\$4o2bobo3b2ob2o3bobo2b4o71b11o7b11o\$11o7b11o71b11o7b11o\$3o3b3o3b2ob2o3b3o3b3o71b3ob3ob3o7b3ob3ob3o\$11o7b11o71b11o7b11o\$4o2bobo3b2ob2o3bobo2b4o71b11o7b11o\$4o2bobo3b2ob2o3bobo2b4o71b11o7b11o\$3ob3ob3o7b3ob3ob3o71b3ob3ob3o7b3ob3ob3o\$11o7b11o71b11o7b11o\$11o7b11o71b11o7b11o\$11o7b11o71b11o7b11o!`
What do you do with ill crystallographers? Take them to the mono-clinic!

calcyman

Posts: 2060
Joined: June 1st, 2009, 4:32 pm

### Re: Challenges

calcyman wrote:B13578/S02468 should be excruciatingly difficult. Without the B8, this is the Fredkin replicator rule (which is reversible ergo has no GoEs), but the B8 makes it irreversible. In particular, the following two patterns have the same descendant...

That 30x30 pattern with two 28x28 predecessors implies at least a 28x28 with two 26x26 predecessors:

`x = 127, y = 27, rule = B13578/S0246811o4b11o31b11o4b11o\$11o4b11o31b11o4b11o\$11o4b11o31b11o4b11o\$3ob3ob3o4b3ob3ob3o31b3ob3ob3o4b3ob3ob3o\$4o2bobo3b2o3bobo2b4o31b11o4b11o\$4o2bobo3b2o3bobo2b4o31b11o4b11o\$11o4b11o31b11o4b11o\$3o3b3o3b2o3b3o3b3o31b3ob3ob3o4b3ob3ob3o\$11o4b11o31b11o4b11o\$4o2bobo3b2o3bobo2b4o31b11o4b11o\$4o2bobo3b2o3bobo2b4o31b11o4b11o\$\$4b2obob2ob2ob2obob2o\$4b2obob2ob2ob2obob2o\$\$4o2bobo3b2o3bobo2b4o31b11o4b11o\$4o2bobo3b2o3bobo2b4o31b11o4b11o\$11o4b11o31b11o4b11o\$3o3b3o3b2o3b3o3b3o31b3ob3ob3o4b3ob3ob3o\$11o4b11o31b11o4b11o\$4o2bobo3b2o3bobo2b4o31b11o4b11o\$4o2bobo3b2o3bobo2b4o31b11o4b11o\$3ob3ob3o4b3ob3ob3o31b3ob3ob3o4b3ob3ob3o\$11o4b11o31b11o4b11o\$11o4b11o31b11o4b11o\$11o4b11o31b11o4b11o!`

(sorry for the weird RLE, I'm away from Golly at the moment).

So what is the smallest MxN bounding box in this rule that contains a pattern with two possible parents? Once that's known, a much larger version of the "more fun solution" described above will give a truly ludicrous upper bound for an explicitly constructible Garden of Eden in B13578/S02468.

dvgrn
Moderator

Posts: 5718
Joined: May 17th, 2009, 11:00 pm

### Re: Challenges

calcyman wrote:
drc wrote:I'm trying to find a rule that's REALLY difficult to find a GoE for.

B13578/S02468 should be excruciatingly difficult. Without the B8, this is the Fredkin replicator rule (which is reversible ergo has no GoEs), but the B8 makes it irreversible.

Actually, the Fredkin replicator rule has the smallest possible GoE: a single cell. Since it has b1, cells are always born around the corners of any pattern. The amount of cells in the next generation then is greater than or equal to the number of corners around the pattern. Almost every pattern has multiple corners, with the only exceptions being zero cells and some infinite-cell patterns. Since infinite patterns need not be proved that they aren't parents for a pattern to be a GoE (see the page on gardens of eden), they need not be considered here. Since no cells can be born from zero cells without b0, the pattern with zero cells cannot become a pattern other than itself, and thus is not a parent of a single cell (Even with b0, it would make a pattern with infinite cells and still not be a parent to the single cell.). As for the remaining finite patterns, since they have multiple corners, they give birth to multiple cells (that is, more than 1). Even if every other cell dies off, these cells will still cause the population to be greater than 1. However, a single cell has a population of exactly 1, so at least 1 cell exists in the resulting pattern that doesn't exist in the single-cell pattern, making it a different pattern. Therefore, the starting patterns do not give birth to the single-cell pattern, and are not parents of the single-cell pattern. Consequently, there are no finite patterns in this rule that give birth to a single cell, making a single cell a GoE.

Since the logic used here only required that a rule have b1, the related B13578/S02468 also has a single cell as a GoE.
`x = 81, y = 96, rule = LifeHistory58.2A\$58.2A3\$59.2A17.2A\$59.2A17.2A3\$79.2A\$79.2A2\$57.A\$56.A\$56.3A4\$27.A\$27.A.A\$27.2A21\$3.2A\$3.2A2.2A\$7.2A18\$7.2A\$7.2A2.2A\$11.2A11\$2A\$2A2.2A\$4.2A18\$4.2A\$4.2A2.2A\$8.2A!`
Gamedziner

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### Re: Challenges

A single cell has this as its predecessor (imagine extending it infinitely):
`x = 256, y = 256, rule = B1357/S02468:T256,256\$2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob3ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o\$2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob3ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o2\$2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob3ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o\$2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob3ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o2\$2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob3ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o\$2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob3ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o2\$2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob3ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o\$2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob3ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o2\$2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob3ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o\$2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob3ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o2\$2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob3ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o\$2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob3ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o2\$2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob3ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o\$2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob3ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o2\$2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob3ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o\$2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob3ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o2\$2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob3ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o\$2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob3ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o2\$2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob3ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o\$2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o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When Calcyman mentioned a bijective correspondence between each pattern and its next generation, I believe he wasn't only referring to finite patterns...

However, under the standard definition you are right, a single cell would be a Garden of Eden. When I noticed this, rather than reporting it, I suspected there was an unconventional solution, because Calcyman usually isn't wrong about these things. Eventually I solved it.

I would like to see a proof that there is a one-to-one correspondence between patterns and their predecessors in Fredkin. It makes for an interesting bi-deterministic rule, yet as you can see from the example, the reverse CA would have infinite neighborhood size as changing a single cell results in differences arbitrarily far away in the previous generation. For this reason, I don't think that the previous generation of an infinite pattern is even well-defined unless the states of all cells are already known, because when building the pattern up cell by cell a change in just one cell can completely alter the previous generation, as you just saw, so doing it repeatedly wouldn't make the previous generation converge to anything.

...Wait, I just found another infinite predecessor of a single cell. So I guess that the set of patterns in the bijective correspondence doesn't include all infinite repeating patterns...
`x = 230, y = 225, rule = B1357/S02468229bo10\$o\$212bo7\$12bo7\$199bo3\$20bo20\$45b2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob3ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o\$45bob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o\$46b2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o\$45b2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob3ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o\$45bob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o\$46b2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o\$45b2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob3ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o\$45bob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o\$46b2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o\$45b2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob3ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o\$45bob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o\$46b2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o\$45b2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob3ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o\$45bob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o\$46b2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o\$45b2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob3ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o\$45bob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o\$46b2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o\$45b2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob3ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o\$45bob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o\$46b2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o\$45b2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob3ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o\$45bob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o\$46b2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o\$45b2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob3ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o\$45bob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o\$46b2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o\$45b2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob3ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o\$45bob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o\$46b2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o\$45b2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob3ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o\$45bob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o\$46b2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o\$45b2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob3ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o\$45bob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o\$46b2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o\$45b2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob3ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o\$45bob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o\$46b2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o\$45b2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob3ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o\$45bob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o\$46b2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o\$45b2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob3ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o\$45bob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o\$46b2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o\$45b2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob3ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o\$45bob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o\$46b2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o\$45b2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob3ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o\$45bob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o\$46b2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o\$45b2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob3ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o\$45bob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o\$46b2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o\$45b2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob3ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o\$45bob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o\$46b2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o\$45b2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob3ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o\$45bob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o\$46b2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o\$45b2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob3ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o\$45bob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o\$46b2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o\$45b2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob3ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o\$45bob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o\$46b2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o\$45b2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob3ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o\$45bob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o\$45bob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o2\$45bob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o\$45bob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o2\$45bob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o\$45bob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o2\$45bob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o\$45bob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o2\$45bob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o\$45bob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o2\$45bob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o\$45bob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o2\$45bob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o\$45bob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o2\$45bob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o\$45bob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o2\$45bob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o\$45bob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o2\$45bob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o\$45bob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o2\$45bob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o\$45bob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o2\$45bob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o\$45bob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o2\$45bob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o\$45bob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o2\$45bob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o\$45bob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o2\$45bob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o\$45bob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o2\$45bob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o\$45bob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o2\$45bob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o\$45bob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o2\$45bob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o\$45bob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o2\$45bob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o\$45bob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o2\$45bob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o\$45bob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o2\$45bob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o\$45bob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o2\$45bob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o\$45bob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o25\$23bo9\$13bo11\$5bo!`

If anyone knows the rules for which patterns are included in the set of patterns that make this rule reversible, I really want to be informed.

gameoflifeboy

Posts: 474
Joined: January 15th, 2015, 2:08 am

### Re: Challenges

I was using the stricter definition of a pattern that cannot appear as a subpattern of generation 1 of any other pattern.

(Formally, you stipulate finitely many ON cells, finitely many OFF cells, and the rest of the universe comprises 'DON'T CARE' cells.)

I seem to recall Achim Flammenkamp uses 'orphan' to refer to the stricter definition and 'GoE' for the weaker definition.

No pattern in Fredkin is an orphan, since running that pattern for 2^n generations (where n is large) will result in multiple well-separated copies of the original pattern. Hence why I suggested B13578/S02468, which does have orphans by the GoE theorem.
What do you do with ill crystallographers? Take them to the mono-clinic!

calcyman

Posts: 2060
Joined: June 1st, 2009, 4:32 pm

### Re: Challenges

dvgrn wrote:
calcyman wrote:B13578/S02468 should be excruciatingly difficult. Without the B8, this is the Fredkin replicator rule (which is reversible ergo has no GoEs), but the B8 makes it irreversible. In particular, the following two patterns have the same descendant...

That 30x30 pattern with two 28x28 predecessors implies at least a 28x28 with two 26x26 predecessors...
(sorry for the weird RLE, I'm away from Golly at the moment).

So what is the smallest MxN bounding box in this rule that contains a pattern with two possible parents?

It's much easier to experiment in Golly than to do the required hard thinking about this (or experimenting in LifeViewer). A more reasonable upper bound seems to be 8x8:

`x = 27, y = 27, rule = B13578/S02468b6o13b6o\$bob2obo13bob2obo\$b2o2b2o13b6o\$b2o2b2o13b6o\$bob2obo13bob2obo\$b6o13b6o14\$ob4obo11bob4obo\$b6o13b6o\$3o2b3o11b3o2b3o\$2o4b2o11b2o4b2o\$2o4b2o11b2o4b2o\$3o2b3o11b3o2b3o\$b6o13b6o\$ob4obo11bob4obo!`

This pair of arrangements allows a birth on B7 in one case and a birth on B8 in the other, while the cells that turn OFF do so because of 5 neighbors in one case and 7 neighbors in the other.

Offhand I don't see how to manage a similar trick without the block of four cells in the center, so maybe 8x8 is minimal. Certainly it seems as if any two patterns with differences in their outside ring of cells can't have the same descendant, so that limits the possibilities quite a bit.

I'll leave someone else to figure out what value of n makes (2^100-1)^(n^2) < 2^((10n-2)^2) -- if I've done the substitution right. Looks like it will take a bit more than an easy afternoon to enumerate all patterns in a square that size, whatever it is...!

No doubt that upper bound can be tightened up quite a bit, just as it can in B3/S23 where the upper bound guarantees a GoE inside 1162907980 by 1162907980 but there's actually one in 10x10.

dvgrn
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### Re: Challenges

gameoflifeboy wrote:If anyone knows the rules for which patterns are included in the set of patterns that make this rule reversible, I really want to be informed.

The patterns you posted are not in Fredkin, but in the very similar rule calcyman posted as a challenge - which is not reversible.

Edit: Please ignore - dvgrn pointed out that these patterns are in Fredkin - I was confused.
Last edited by wildmyron on July 20th, 2017, 11:58 pm, edited 1 time in total.
The latest version of the 5S Project contains over 183,000 spaceships. Tabulated pages up to period 160 are available on the LifeWiki.
wildmyron

Posts: 1176
Joined: August 9th, 2013, 12:45 am

### Re: Challenges

wildmyron wrote:
gameoflifeboy wrote:If anyone knows the rules for which patterns are included in the set of patterns that make this rule reversible, I really want to be informed.

The patterns you posted are not in Fredkin, but in the very similar rule calcyman posted as a challenge - which is not reversible.

Don't know if those two patterns got edited, but they certainly work in Fredkin, and the rule header specifies Fredkin now -- no B8 to be seen.

I'm also curious about the best way to state the inverse rule, for either Fredkin or the related B1357/S1357 (which makes eight copies of any pattern at sufficiently high 2^k-tick intervals, instead of nine copies.)

It seems fairly simple to reverse any pattern that is in fact Generation N of some other pattern: just run it for the lowest power-of-two number of ticks that's larger than the largest diameter of the pattern, inspecting it after each tick to see if it's made up of eight (Replicator) or nine (Fredkin) copies of some smaller pattern. The number of cells separating copies at opposite edges is twice the number of ticks that have passed since the smaller pattern appeared at the center of gravity between those copies. Any tick between then and now can be trivially reconstructed.

But there are a lot of patterns that can't be run backward -- right? What would the T=-1 generation of something asymmetrical be, like

Code: Select all
`x = 5, y = 5, rule = B13578/S02468obo2\$obobo2\$obobo!#C [[ THUMBNAIL THUMBSIZE 2 ]]`

?

dvgrn
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### Re: Challenges

dvgrn wrote:
wildmyron wrote:
gameoflifeboy wrote:If anyone knows the rules for which patterns are included in the set of patterns that make this rule reversible, I really want to be informed.

The patterns you posted are not in Fredkin, but in the very similar rule calcyman posted as a challenge - which is not reversible.

Don't know if those two patterns got edited, but the certainly work in Fredkin, and the rule header specifies Fredkin now -- no B8 to be seen.

Whoops, my mistake, I confused B8 with S8.
The latest version of the 5S Project contains over 183,000 spaceships. Tabulated pages up to period 160 are available on the LifeWiki.
wildmyron

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Joined: August 9th, 2013, 12:45 am

### Re: Challenges

drc wrote:A glider that reaches its maximum population 1 generation before its minimum

Done:
`x = 23, y = 6, rule = B34e5y7e/S23bo5bo6b3o3b3o\$2obobob2o8bobo\$9o\$bo2bo2bo10bo\$b2o3b2o7b3ob3o\$2bo3bo8b2o3b2o!`
`x = 11, y = 5, rule = B2ck3-ij5n78/S01e2ei3-k5ai8b2o\$2o3b2o\$bo4bo3bo\$2bo2b2o\$o7bo!`

(Check Gen 2)

toroidalet

Posts: 967
Joined: August 7th, 2016, 1:48 pm
Location: my computer

### Re: Challenges

Find the slowest spaceship in ANY rule.
One big dirty Oro. Yeeeeeeeeee...

gameoflifemaniac

Posts: 752
Joined: January 22nd, 2017, 11:17 am
Location: There too

### Re: Challenges

That would just mean using AbhpzTa's rule, or A For Awesome's variant for many millions of cells, and that would already beat all records. There is no slowest ship, because any n for C/n is possible.
Things to work on:
- Find a (7,1)c/8 ship in a Non-totalistic rule (someone please search the rules)
- Find a C/10 in JustFriends
- Find a C/10 in Day and Night
AforAmpere

Posts: 1019
Joined: July 1st, 2016, 3:58 pm

### Re: Challenges

I meant the slowest speed you CAN make. Extending the c/2n(+1) is trivial, you have to keep the population low.
One big dirty Oro. Yeeeeeeeeee...

gameoflifemaniac

Posts: 752
Joined: January 22nd, 2017, 11:17 am
Location: There too

### Re: Challenges

gameoflifemaniac wrote:I meant the slowest speed you CAN make. Extending the c/2n(+1) is trivial, you have to keep the population low.

If you don't say exactly how low to keep the population, there's still no good way to answer this challenge.

Constructs like the Parallel HBK, not to mention the Demonoid and Orthogonoid spaceships, can be made arbitrarily slow by separating the two parts of the ship -- and there's no increase in population, only in bounding box.

dvgrn
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Joined: May 17th, 2009, 11:00 pm

### Re: Challenges

Is there a slowest possible spaceship for n cells?
If you're the person that uploaded to Sakagolue illegally, please PM me.
`x = 17, y = 10, rule = B3/S23b2ob2obo5b2o\$11b4obo\$2bob3o2bo2b3o\$bo3b2o4b2o\$o2bo2bob2o3b4o\$bob2obo5bo2b2o\$2b2o4bobo2b3o\$bo3b5ob2obobo\$2bo5bob2o\$4bob2o2bobobo!`

(Check gen 2)

Saka

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Joined: June 19th, 2015, 8:50 pm
Location: In the kingdom of Sultan Hamengkubuwono X

### Re: Challenges

Saka wrote:Is there a slowest possible spaceship for n cells?

Well, yes, for small N these do exist, of course. But there's not ever going to be a discoverable algorithm where you input N and get back the relevant slowest possible spaceship.

Above some value Nmax < pop(0hd Demonoid) there isn't any slowest possible spaceship, and we'll never know what Nmax is -- we'll just have an upper bound based on the lowest-population Demonoid/Orthogonoid-ish thing that anyone has built so far.

It will always be possible that there's an incredibly lucky/clever shortcut for self-construction that nobody has happened to come across yet -- maybe one that would take an exhaustive search of 1000x1000 bounding boxes to find. (Even a million-qubit quantum computer might not be up to that search task, in practice...!)

dvgrn
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### Re: Challenges

Challenge: Find a pattern that doesn't die out in R6,C0,M1,S34..58,B34..45,NM, which I am terming "Bugs but I literally changed the range to 6 and it's still miraculously stable."
`x = 11, y = 5, rule = B2ck3-ij5n78/S01e2ei3-k5ai8b2o\$2o3b2o\$bo4bo3bo\$2bo2b2o\$o7bo!`

(Check Gen 2)

toroidalet

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