BlinkerSpawn wrote:muzik wrote:If we let this run infinitely, will it ever become periodic, or will it grow chaotically forever, eventually producing negatives of basically every pattern known like gemini?Code: Select all`x = 1, y = 1, rule = B123478/S01234678`

o!

If you look at it even in LifeViewer you'l notice that the corners start producing a sort-of-agar basically right away, so no.

Yup, by right about T=8000 this particular pattern becomes completely predictable.

In general this kind of question can't be categorically answered yes or no, I think, unless you can run the pattern far enough that you can catalogue all the units of repetition and all the periods, and show that they will never interact in any novel ways at any later time. A starting pattern may not be much more complicated than this before some multi-puffer interaction will turn out to be an "infinite novelty generator", which seems to keep generating new chaotic combinations indefinitely.

In those cases it's hard to show that those combinations might not somehow manage to do something like what the Sparse Life early universe does -- generate more and more complex glider collisions, so that the farther out you look, the more new things you see. Doesn't seem like there's an easy way to prove absolutely that something like a Gemini will never ever show up out there.

You can certainly say that there's a near-zero probability of any such thing happening if the average ash density is high, as it seems likely to be in variations of the above pattern. It's just hard to get from an estimate of infinitesimally low probability that something Gemini-sized will ever crawl out of that kind of soup, to an actual proof of zero probability.