Changing the rules (part 3)

Take a look at a pre-loaf and a pi:screen-shot-2016-09-07-at-11-37-22-pm

If you run them in B37c/S23, the pre-loaf stabilizes quickly, but the pi takes a while — and some space. It needs 110 generations to settle down.

If you run them in B37e/S23, though, the pre-loaf just becomes a loaf immediately and the pi stabilizes much more quickly, in only 23 generations, and without spreading out so much.

So based on that, maybe it’s plausible B37c/S23 could be explosive while B37e/S23 isn’t. And then that might help account for why B37/S23 is explosive while B36/S23 and B38/S23 aren’t.

But this is still rather hand-wavy. Plausible is one thing, proved is something else entirely. First, it’s not just what happens to these objects that matters, but also how likely they are to arise in the first place. No matter how long and over what area a pi evolves, it won’t cause anything if it never crops up in the first place.

Second, in addition to pre-loafs and pis, you also need to consider larger sub-patterns with pre-loaves and pis embedded in them. How likely are they and what do they do under the two rules?

Anyway, proof or no proof, B37e/S23 really isn’t explosive. That means — unlike B37/S23 — it can be explored with a soup search. But apgmera, the C++ version 3 of apgsearch, can’t handle non-totalistic rules. The Python version 1.0 can, or rather a hacked version of it can. Slowly! I’ve been running it and it’s done 2 or 3 soups per second, about 3 orders of magnitude slower than apgmera can run B3/S23. And for some reason it seemed not to be sending results to Catagolue.*

But anyway, 11c/52 diagonal puffers cropped up several times, laying trails of blocks and loaves:

screen-shot-2016-09-07-at-11-49-25-pmThis puffer evolves from this 7 cell object:screen-shot-2016-09-07-at-11-54-50-pmAnd if there’s a suitably placed ship nearby, it becomes an 11c/52 diagonal spaceship. This has cropped up in several soups.screen-shot-2016-09-07-at-11-44-59-pm

*Edit: My B37e/S23 hauls are on Catagolue, but under the enharmonic name B37-c/S23.

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Changing the rules (part 2a)

That lame explanation seems even more lame when you consider this: The non totalistic rule B37c/S23 (meaning birth occurs if there are 3 live neighbors, or if there are 7 live neighbors with the dead neighbor in the corner of the neighborhood) is explosive, but B37e/S23 (birth occurs if there are 3 live neighbors, or if there are 7 live neighbors with the dead neighbor on the edge of the neighborhood) isn’t.

Changing the rules (part 2)

Here’s an even more perplexing (to me, at least) instance of different CA behavior under similar-but-different rules. Consider this 32 x 32 soup:Screen Shot 2016-09-04 at 10.14.02 AM B36/S23 is a Life-like rule sometimes called HighLife. Many objects behave the same way as in Life; in particular, blocks, loaves, boats, and beehives are still lifes; blinkers are p2 oscillators; gliders are c/4 diagonal spaceships. So after 378 generations in B36/S23 when that soup looks like this, it’s stabilized:Screen Shot 2016-09-04 at 10.10.26 AM B38/S23 has no nickname I know of. Under that rule, the same soup stabilizes in 483 generations:Screen Shot 2016-09-04 at 10.10.52 AM And in B37/S23… here’s what it evolves to after 10,000 generations:Screen Shot 2016-09-04 at 10.11.08 AMPopulation 17,298 and growing, presumably forever.

Fairly typical. I’ve seen some soups take several thousand generations to stabilize in B38/S23, and I’ve seen a few — very few — stabilize in B37/S23. But most soups stabilize in 1000 generations or so in B36/S23 and B38/S23… and almost all soups explode in B37/S23.

Does that make any sense to you? Explain it to me, then.

I guess you can wave your hands and say “well, if you have few births you don’t get explosive behavior, and if you have many births in some small region you get momentary overpopulation which then crashes in the next generation, but somewhere in the middle there’s a point where you have not too few births but not enough crashes and it explodes”. But is that the best we can do at understanding this?

Edit: In fact, that lame explanation seems even more lame when you consider this: The non totalistic rule B37c/S23 (meaning birth occurs if there are 3 live neighbors, or if there are 7 live neighbors with the dead neighbor in the corner of the neighborhood) is explosive, but B37e/S23 (birth occurs if there are 3 live neighbors, or if there are 7 live neighbors with the dead neighbor on the edge of the neighborhood) isn’t.