1to5

[Linicks]

Hi Guys,

Try this for size. Needs to be run slowly (1s), one step at a time to see the pattern - but let it run.

Code: Select all

#GLF 1.0
x = -30, y = -20

bbbbobbbb$
bbobobbbb$
bbbbbbbbb$
bbbobbbbb$
bbobobbbb$
bbbbbbobb$
bbbbbbbbb$
bbbbbbbbbbbb$
bboooobbbbbb$
oboobbbbbbbb$
bboboobbbbbb$
bbbobooobbbb$
obbbbbobbbbb$
obbobbobbbbb$
bbbbbbbbbbbb$
bbbbbbbbbbbbbbbb$
bbbbbbobbbobbbbb$
bbobbobobobbbbbb$
bbbbbobbbobobbbb$
bobobbbobbbbbbbb$
bbbbooobobbbbbbb$
bobbbbooooobbbbb$
bbbobobbbbbobbbb$
bboooboboobbbbbb$
bobobobbobobbbbb$
bbbbbbbbbbbbbbbb$
bbbbbbbbbbbbbbbbbbbb$
bbbbbbobbbbobobbbbbb$
bbobooooooooobbbbbbb$
bbbooobbbbbbobobbbbb$
bbbbooobbbbbobbbbbbb$
bbbbbobobbboobobbbbb$
bbbbbobboobobobbbbbb$
bbbobbobboobbbbbbbbb$
bbbbbbbbobboobbbbbbb$
bbbbooobbbbbbbobbbbb$
bbboboobbbooobobbbbb$
bbbbbobbbbbbbbbbbbbb$
bbbobbobooboobobbbbb$
bbbbbbbbbbbbbbbbbbbb$
bbbbbbbbbbbbbbbbbbbbbbbb$
bbbbbbbbbbbboboobbbbbbbb$
bbbobobbooooobooobbbbbbb$
bbbobooobbobbooobbbbbbbb$
bbbbbobbbbobbbbobbbbbbbb$
bbbbbboobboobboobbbbbbbb$
bbbobobobbbobbbobobbbbbb$
bbbbbbooboobooobbbbbbbbb$
bbbbobobbboobobbobbbbbbb$
bbbobbooobbbbbbbobbbbbbb$
bbbbbobbooobbboobbbbbbbb$
bbbobbbbboooooooobbbbbbb$
bbbbbbbbbbbooboobobbbbbb$

Or perhaps 10 steps?

Code: Select all

#GLF 1.0
x = -23, y = -23

bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb$
bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb$
bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb$
bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb$
bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb$
bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb$
bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb$
bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb$
bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb$
bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb$
bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb$
bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb$
bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb$
bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb$
bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb$
bbbbbbbbbbbbbbbbbbbbobbbbbbbooboobobbbbbbbbbbbb$
bbbbbbbbbbboobbbbbbbbbbbbboooooboobbbbbbbbbbbbb$
bbbbbbbbbbbbbbbbbbooobooboboobobobbobbbbbbbbbbb$
bbbbbbbbbbbbboboboboboboobbobbbobbbbbbbbbbbbbbb$
bbbbbbbbbbbbobbobbbbobobbobbbbboobbbbbbbbbbbbbb$
bbbbbbbbbbbbbbbbboobbbobbbbboboobobobbbbbbbbbbb$
bbbbbbbbbbbboobooobboobobobbobobobobbbbbbbbbbbb$
bbbbbbbbbbbbbbbobbboobobooboboobbooobbbbbbbbbbb$
bbbbbbbbbbbboooobbobobbobbbobbobbboobbbbbbbbbbb$
bbbbbbbbbbbbbbbbbbbbobbobobbboboobobbbbbbbbbbbb$
bbbbbbbbbbbobobbboboboboobbobobbbbobbbbbbbbbbbb$
bbbbbbbbbbboboobbobbbbobbboobbbobbbbbbbbbbbbbbb$
bbbbbbbbbbbbboobobboooobboobbbbbbobbbbbbbbbbbbb$
bbbbbbbbbbbbobbboobbobboobobboboobbbbbbbbbbbbbb$
bbbbbbbbbbbbobooobbboobobbbbooooobobbbbbbbbbbbb$
bbbbbbbbbbbbboobobooboobboobobobbbbbbbbbbbbbbbb$
bbbbbbbbbbboboobbbbbbbbbbbbobbboobobbbbbbbbbbbb$
bbbbbbbbbbbobbboboobbooobbbooobbbbobbbbbbbbbbbb$
bbbbbbbbbbbbboooboooooobbbobboooobbbbbbbbbbbbbb$
bbbbbbbbbbbbbbooooobbbobbbbboboobobbbbbbbbbbbbb$
bbbbbbbbbbbbobbboobobbobbbbobbbbbbbbbbbbbbbbbbb$
bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb$
bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb$
bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb$
bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb$
bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb$
bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb$
bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb$
bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb$
bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb$
bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb$
bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb$

Nick
EDIT: See my reply why I edited this.

[Bullet51]

Welcome to the forum!

[Linicks]

Thanks,

BTW, I forgot to mention - run 1to5 and you will get the numbers 1,2,3,4,5 generated, then after that a bit of life, then a 5 cell glider with 4 other still life = 5 - and the starting gen 0 is 5 blocks.

Nick

[dvgrn]

BTW, I forgot to mention - run 1to5 and you will get the numbers 1,2,3,4,5 generated...

What program are you using to do the backtracking? Is it the mysterious GLF 1.0?

There's a JavaScript app called LifeViewer that can preview patterns in the browser, but it will be happier if you make a few changes to your RLE format. As it stands, Golly can display your pattern, but LifeViewer can't (though that may change in a few weeks -- thanks for the test case!)

Standard format would be more like this:

Code: Select all

#CXRLE Pos=-30,-20
#GLF 1.0
x = 18, y = 53, rule = B3/S23
bbbbobbbb$
bbobobbbb$
bbbbbbbbb$
bbbobbbbb$
bbobobbbb$
bbbbbbobb$
bbbbbbbbb$
bbbbbbbbbbbb$
bboooobbbbbb$
oboobbbbbbbb$
bboboobbbbbb$
bbbobooobbbb$
obbbbbobbbbb$
obbobbobbbbb$
bbbbbbbbbbbb$
bbbbbbbbbbbbbbbb$
bbbbbbobbbobbbbb$
bbobbobobobbbbbb$
bbbbbobbbobobbbb$
bobobbbobbbbbbbb$
bbbbooobobbbbbbb$
bobbbbooooobbbbb$
bbbobobbbbbobbbb$
bboooboboobbbbbb$
bobobobbobobbbbb$
bbbbbbbbbbbbbbbb$
bbbbbbbbbbbbbbbbbbbb$
bbbbbbobbbbobobbbbbb$
bbobooooooooobbbbbbb$
bbbooobbbbbbobobbbbb$
bbbbooobbbbbobbbbbbb$
bbbbbobobbboobobbbbb$
bbbbbobboobobobbbbbb$
bbbobbobboobbbbbbbbb$
bbbbbbbbobboobbbbbbb$
bbbbooobbbbbbbobbbbb$
bbboboobbbooobobbbbb$
bbbbbobbbbbbbbbbbbbb$
bbbobbobooboobobbbbb$
bbbbbbbbbbbbbbbbbbbb$
bbbbbbbbbbbbbbbbbbbbbbbb$
bbbbbbbbbbbboboobbbbbbbb$
bbbobobbooooobooobbbbbbb$
bbbobooobbobbooobbbbbbbb$
bbbbbobbbbobbbbobbbbbbbb$
bbbbbboobboobboobbbbbbbb$
bbbobobobbbobbbobobbbbbb$
bbbbbbooboobooobbbbbbbbb$
bbbbobobbboobobbobbbbbbb$
bbbobbooobbbbbbbobbbbbbb$
bbbbbobbooobbboobbbbbbbb$
bbbobbbbboooooooobbbbbbb$
bbbbbbbbbbbooboobobbbbbb!

The only change that LifeViewer really needs is to specify the height of the pattern in the header: y = 53.

If you want to say that the pattern's upper left corner is at (-30,-20), you can do that at least for Golly with the #CXRLE Pos=-30,-20 line.

Traditionally in RLE format there's a "rule = " parameter in the header, in this case "rule = B3/S23". Also there isn't a blank line after the header, and the RLE encoding ends with an exclamation point. None of those will bother either LifeViewer or Golly, but other Life programs might possibly have trouble with them.

Your pattern is really more like picture format than RLE -- there isn't any actual Run Length Encoding. If you want the pattern to be more visible for some reason, it doesn't hurt to post it that way, though usually people use asterisks for ON cells and periods for OFF cells in that case.

Code: Select all

#P-30,-20
....*....
..*.*....
.........
...*.....
..*.*....
......*..
.........
............
..****......
*.**........
..*.**......
...*.***....
*.....*.....
*..*..*.....
............
................
......*...*.....
..*..*.*.*......
.....*...*.*....
.*.*...*........
....***.*.......
.*....*****.....
...*.*.....*....
..***.*.**......
.*.*.*..*.*.....
................
....................
......*....*.*......
..*.*********.......
...***......*.*.....
....***.....*.......
.....*.*...**.*.....
.....*..**.*.*......
...*..*..**.........
........*..**.......
....***.......*.....
...*.**...***.*.....
.....*..............
...*..*.**.**.*.....
....................
........................
............*.**........
...*.*..*****.***.......
...*.***..*..***........
.....*....*....*........
......**..**..**........
...*.*.*...*...*.*......
......**.**.***.........
....*.*...**.*..*.......
...*..***.......*.......
.....*..***...**........
...*.....********.......
...........**.**.*......

If you copy and paste into Golly and then back out again, you'll get a compressed version with lines up to 70 characters long, like this:

x = 18, y = 53, rule = B3/S23
4bo$2bobo2$3bo$2bobo$6bo3$2b4o$ob2o$2bob2o$3bob3o$o5bo$o2bo2bo3$6bo3bo
$2bo2bobobo$5bo3bobo$bobo3bo$4b3obo$bo4b5o$3bobo5bo$2b3obob2o$bobobo2b
obo3$6bo4bobo$2bob9o$3b3o6bobo$4b3o5bo$5bobo3b2obo$5bo2b2obobo$3bo2bo
2b2o$8bo2b2o$4b3o7bo$3bob2o3b3obo$5bo$3bo2bob2ob2obo3$12bob2o$3bobo2b
5ob3o$3bob3o2bo2b3o$5bo4bo4bo$6b2o2b2o2b2o$3bobobo3bo3bobo$6b2ob2ob3o$
4bobo3b2obo2bo$3bo2b3o7bo$5bo2b3o3b2o$3bo5b8o$11b2ob2obo!

[Linicks]

Thank you very much, what a brilliant reply! I didn't know about the Golly copy-back-to-file thing to sort out the pattern - great stuff!

Code: Select all

x = 18, y = 53, rule = B3/S23
4bo$2bobo2$3bo$2bobo$6bo3$2b4o$ob2o$2bob2o$3bob3o$o5bo$o2bo2bo3$6bo3bo
$2bo2bobobo$5bo3bobo$bobo3bo$4b3obo$bo4b5o$3bobo5bo$2b3obob2o$bobobo2b
obo3$6bo4bobo$2bob9o$3b3o6bobo$4b3o5bo$5bobo3b2obo$5bo2b2obobo$3bo2bo
2b2o$8bo2b2o$4b3o7bo$3bob2o3b3obo$5bo$3bo2bob2ob2obo3$12bob2o$3bobo2b
5ob3o$3bob3o2bo2b3o$5bo4bo4bo$6b2o2b2o2b2o$3bobobo3bo3bobo$6b2ob2ob3o$
4bobo3b2obo2bo$3bo2b3o7bo$5bo2b3o3b2o$3bo5b8o$11b2ob2obo!

Long story follows... this is what the Internet can do for you:

As to the reverse engineering generator, this was sparked off by a crossword forum I use (I do hard crosswords, like the Listener, Azed etc.):

http://www.boards2go.com/boards/board.c ... =dharrison

I replied at the end of the thread that to back engineer GOL is almost impossible... it appears so if you read the setters blog:

http://listenwithothers.com/2015/11/09/ ... harribobs/

Well, when I was looking into the puzzle, I have and used GTKLife (this is the GLF file header):

http://ironphoenix.org/gtklife/

to suss out the pattern. It turns out that the author of GTKLife runs a on-line 'scrabble challenge' site:

http://ironphoenix.org/scrabble/

I e-mailed a fellow crossword fan about the scrabble site, and by-the-way he said I have read your post about GOL, I have written a program that can back engineer GOL... do you want a copy?

YES PLEASE!

Since then, he worked it (on my input) so it can knock out reverse back generations (takes ages after =>10). The man is a genius (in Golly, see -> wireworld->primes.mc)

http://www.quinapalus.com/

Anyway, so here we are. I told him to publish it 'official'. As soon as he has, I will post here. It is magic.

Chaos to life:

Code: Select all

x= 23, y = 20, rule = B3/S23
16bob2o$o3bobo3b2ob2o2b5o$2bo8b2o2b2o3bo$obobo2bobob2obobo3bobo$7b2o8b
2o$b4obobobo4bo2b2o$3b2obo4bob3obobobo$4bo2bo3b2o6b2o$2obo3bo2b2o2bobo
4bo$6bo9bo2b2o$2o3b2ob3o2bob3ob3o$3b4obobo9b2o$2b2o4bob5obobo$2bob7o2b
ob2o5bo$2bo3bo10b3o$2bo9bo2bo3bobo$b2o2b3ob3o2bo5bobo$2b2o2bob4o2b2ob
4o$bo2bo8bo2bo2b2o$2bo4b2o4bo3bo!

Nick

[praosylen]

You can also generate them manually, although it's harder:

Code: Select all

x = 49, y = 11, rule = B3/S23
40bo$30bo11bobo$16bo23bobobobobo$o5bobo17bobobo9bo5bobo$o6bo6bobobo13b
o10bo$o14b3o10bo2bo11bo3bo$o5bobo4bobobobo6b3ob3o7bob2ob2o$o6bo2bo2bob
o3bo6bo3bo10bo3bo2bo$18bo8bo2b2o10b2obo$8bo7bo12b2o14bo$17bo13bo14b2o!

[Linicks]

You can also generate them manually, although it's harder:

Sorry, don't get it - what's 'them'?

Nick

[danieldb]

You can also generate them manually, although it's harder:

Sorry, don't get it - what's 'them'?

Nick

the number 1

[praosylen]

You can also generate them manually, although it's harder:

Sorry, don't get it - what's 'them'?

Nick

Predecessors for patterns (in this case, the 1).

[dvgrn]

Since then, he worked it (on my input) so it can knock out reverse back generations (takes ages after =>10).

It's always interesting to see what approaches people take to these kinds of problems. Occasionally a new algorithm comes along that has a big edge over previous attempts.

If ten ticks is the current practical limit, then it sounds as if the program is probably doing pretty much the same thing as lifesrc/WLS/JLS have been able to do for a good while now. Here's a sample from Alan Hensel's pattern collection from twenty years ago:

Code: Select all

x = 68, y = 46, rule = B3/S23
17bo$14bo3bo3b2o$16bo3bo$15bo3bo3b2o$13bo3bo3bo$8bo2bo2bo3bo3bobo$10bo
5bo3bo$4bo3bo6bo3bo$2bo3bo5bo4bo3bo$bo3bo3bo3bo4bo47bo$3bo3bo53bobo3bo
$o3bo3bo3bobo3bo42bo3bo$2bo3bo3bo5bo47bo$bo3bo3bo5bo46bo3bo$3bo3bo3bob
o46bo2bo$o3bo3bo6bo22bo19bo$2bo3bo3bo3bo8bo4bo3bo2bo3bo3b2o2bobo2b2o3b
o3bo2bo$5bo3bo2bo5bo6bo3bobo5bo3bo13bo3bo3bo$bobo3bo5bo2bo3bo2bo3bo8bo
3bo3b2o2bo2b2o3bo3bo$3bo7bo5bo3bo4bo5bobo3bo3bo5bo5bo3bo3bo$bo3bobo7bo
3bo4bo3bo2bo3bo3bo3bobo5bobo3bo3bo$10bo2bo4bo3bo2bo11bo3bo13bo3bo$3bo
7bo4bo3bo6b2o2bobo2bo3bo6bobo6bo3bo$bo2bobo6bo3bo3bo16bo3bobo4bobo2bo
3bo$2bo6bo9bo5bo4bo3bo4bo7bo3bo5bo$7bo3bo4bobo4bo3bo4bo9bobo3bo$6bo3bo
4bo8bo3bo2bo3bobo3bo4bo3bo2bobo$8bo3bo6bo2bo3bo6bo4bo6bo3bo8bo$5bo3bo
3bo4bo2bo3bo3bo6bo3bo2bo3bo3bo3bo$7bo3bo4bo6bo3bo4bo2bo3bo4bo3bo3bo3bo
bo$6bo3bo2bo3bo3bo2bo3bo2bo5bo3bo4bo3bo3bo$8bo6bo10bo7bo3bo6bo3bo5bo$
36bo3bo2bo3bo3bo$8bobo3bo20bo3bo8bo4bo$11bo25bo14bo2bobo$9bo3bo36bo6bo
bo$8bo3bo36bo5bo3bo$10bo3bo37bo3bo$7bo3bo42bo3bo$9bo3bo39bo3bo$8bo3bo
38bo3bo3bo$10bo41bo3bo3bo$54bo3bo$53bo3bo$55bo3bo$56bo!
[[ THEME 4 THUMBNAIL AUTOSTART PAUSE 2 GPS 10 LOOP 100 ]]

Finding a good algorithm for sorting out predecessors with specific characteristics -- smallest possible, fewest ON cells, comes from greatest possible distance from ending position, etc. -- is still a big topic of research... or at least a potential topic of research, as soon as someone can figure out a good approach.

The search space is just plain too big to do exhaustive searches on, and B3/S23 seems to be unpredictable enough that it's difficult even to develop rules of thumb for which branches of the tree to follow, that are any significant improvement over just picking randomly. Here's a recent attempt to develop better backtracking heuristics, by simsim314.

[simeks]

I wrote a backtracking program a while back. I never quite completed it, but I just wanted to see what it would do with this idea...

Code: Select all

x = 15, y = 13, rule = Life
5bo$4bo$3bo$3b2o8bo$2ob3o5b3o$b2obo6b2o$6b3o4bo$8bo3bo$6bo5b2o$6b2o5bo
$5b3o4bo$14bo$8bo3b2o!

Is this result about what you would expect from the programs dvgrn mentioned above (lifesrc/WLS/JLS), or would it be worth the trouble to try to complete it?

[Linicks]

To give you an idea, the code I have is in C, and only 139 lines.

'Tis magic.

Nick

[Linicks]

OK, the code I used to do snoitareneg has now been published:

http://www.quinapalus.com/unlife.html

Nick

[dvgrn]

I wrote a backtracking program a while back. I never quite completed it, but I just wanted to see what it would do with this idea...
[... very reasonable-looking 15-tick predecessor of "15" pattern]
Is this result about what you would expect from the programs dvgrn mentioned above (lifesrc/WLS/JLS), or would it be worth the trouble to try to complete it?

It looks surprisingly good to me. People with a lot of experience with lifesrc variants might be able to produce an equivalent result, but I think it might be difficult to do without spending a lot of time manually customizing search areas and settings.

It seems like a good sign that the predecessor doesn't just look like deeply interconnected "space dust". Working a little further backward in time, one could imagine predecessors of the right side, bottom, and top left moving away from the central "15" site, and each part becoming separately glider-constructible. It's wishful thinking, sure, but if the population can be kept low enough, eventually a predecessor will be spread out over enough space that there'd be room to work on a construction.

It's very interesting that the backtracking algorithm was able to find predecessors that don't increase in size monotonically at higher negative T values. The bounding box drifts down a few cells, then up a few cells, especially between T=-10 and T=-8. Was that a deliberate part of the search conditions, or just an artifact of trying to minimize bounding box and/or population of predecessors?

[simeks]

Was that a deliberate part of the search conditions, or just an artifact of trying to minimize bounding box and/or population of predecessors?

I had go back to the source code to remember exactly what it does...

There was no deliberate attempt to control the result, just a cost function which uses the sum of the number of on-cells and the number of off-cells that is in the Moore neighbourhood of an on-cell (the green and red cells in the pattern below). For generation 0 the cost would thus be 139. This seems to give a bit more interesting results than just the population count.

For each new generation the program pools a number of the best predecessors, for this search I pooled 1000 predecessors for each generation.

Then it generates predecessors for each of these 1000 patterns, and pools the 1000 of these with the best overall score, with the condition added that a single pattern of the 1000 in one generation may generate at most 300 of the predecessors in the next pool, just to keep some variety of ancestry.

For each pattern, all possible predecessorn are generated that have all their on-cells within a certain area. To keep that to a reasonable number I use an area made up the on-cells of the current generation, off-cells in the Moore neighbourhood of on-cells, and to that I usually add cells with exactly two cells of their von Neumann neighbourhood already in the area so far (the blue cells in the pattern), which makes it a bit more interesting without increasing the search space too much.

If a pattern has too many predecessors in this area it is ignored. I used a threshold value of 500000 in this search.

The running time was about 2 hours for 15 generations of this pattern.

Code: Select all

x = 17, y = 15, rule = LifeHistory
4.B3D$3.B2DAD$3.2DA2D$2.BDA2D5.B3D$4D2A2D3.3DAD$D2AD3ADB.BD3AD$2D2ADA
6D2A2D$B6D3A4DAD$5.B3DAD.DA2D$5.BDA3D.D2AD$5.2D2ADB.2DADB$5.D3ADB.DA
3D$5.6D.3DAD$7.BDAD.D2A2D$8.3D.4DB!

EDIT:
Some further tweaking of search parameters finds this population 33, generation -15 predecessor of the "15" pattern (which incidently has population 15):

Code: Select all

x = 16, y = 9, rule = LifeHistory
A.A2.A4.A$2.A.2A.A.A.A.A.A$4.2A2.2A3.2A$5.2A3.A.2A$4.2A$5.A4.A$8.A.A.
A$6.2A$8.A!

[simeks]

Some further tweaking of search parameters finds this population 33, generation -15 predecessor of the "15" pattern (which incidently has population 15):

This soup says something about how far that probably still is from the lowest population predecessors that exist...

In that soup the canoncal eater2 (population 19) has a predecessor 85 generations back, with the same population as the end result:

Code: Select all

x = 9, y = 10, rule = LifeHistory
.A$A.A$2.2A$A3.A$2A.2A2$4.A.A$2.A5.A$2.A3.2A$2.A!