More on puffers in high-count Life variants

[mmcirvin]

The "pond puffer" I mentioned earlier for the B37/S23 rule also exists in B37/S238, along with the other puffer. (In cellular-automaton terminology, a puffer is something that moves along leaving debris behind, and a breeder is, broadly, a thing that makes things that make things; in this case it's a modified puffer that shoots puffers that leave debris.) I've found nice precursor patterns for both of them made of pairs of R-pentominoes that look like impending Atari 2600 plane crashes (if you have Golly you can select the grids and copy and paste them in directly):


puffer 1, B37/S23 or B37/S238

O.....O
OOO.OOO
.O...O.

puffer 2 (pond puffer), B37/S23 or B37/S238

O.........O
OOO.....OOO
.O.......O.

In regular Life, they both die out without creating so much as a glider.

But I haven't found a way to perturb that precursor to puffer 1 to get the naturally occurring B37/S238 breeder that is a perturbation of puffer 1. The smallest precursor of the breeder I've been able to find is this:

breeder, B37/S238

...........O
...........O
...........O
............
............
............
..OOO.OOO...
OO..O.O..OO.
.OOO...OOO..
..O.....O...

The bottom part by itself becomes puffer 1.

Conway Life has lots of puffer and breeder patterns, but none that occur "naturally" as common protrusions of random soups. This also seems to be the case in B23/S238. It's tempting to conjecture that there is some causal connection between the existence of common natural puffers in B237/S23 and B237/S238, and the fact that sufficiently large soups in these automata always become ever-growing chaos. But I don't know if there is one, aside from both facts arising from high-number birth and survival rules.


ikkyu2 asked if all of this work was for something, or if it was studied simply for its own sake. Really it's the latter; this is recreational, or, if you prefer, pure mathematics. Researchers in various fields do occasionally value cellular automata as a kind of very simple idealized "physics" that you can use to prove points about how little you need to set up a system that does X or Y; that was more or less what von Neumann was up to back in 1948. Occasionally someone like Ed Fredkin or Stephen Wolfram insists that they have some sort of cosmic significance. And, while I haven't used it, there seems to be a small music sequencer for the iPhone that uses the Wireworld CA as its control architecture.

But mostly people study them because they're kind of cool, like small natural universes that you can study in detail with readily available equipment.

Comments

[ronebofh.livejournal.com]

oh6 has also been fooling around with Life lately.

[mmcirvin.livejournal.com]

I think Golly has really revolutionized the field; before it there were Life implementations with nice user interfaces and Life implementations with super-fast engines, but not both. And it's free, open-source and cross-platform.

[mmcirvin.livejournal.com]

...One thing I do wish is that Golly had a way to switch its clipboard copy into producing an ASCII-art clipping like the ones I've put in this LJ post. It'll accept them as pasted patterns, but when you do a copy, what you get is in the Life hobbyists' RLE standard--which can be conveniently pasted into a textual post, and is nice and small, but is not human-readable.

[(Anonymous)]

It would be pretty easy to write a Python/Perl script to produce an ASCII-art version of the current selection. (I'm unlikely to add that feature as a built-in option because it only works for 2-state universes.)

Re: More on puffers in high-count Life variants

[(Anonymous)]

I've added a script called copy-as-text.py to the Golly Scripts Database that should do what you want. Go to Help > Online Archives to download it. You can also use Preferences > Keyboard to assign a shortcut like alt-C to run the script.

Re: More on puffers in high-count Life variants

[mmcirvin.livejournal.com]

Awesome! Thanks!

Smaller precursor to the B37/S238 breeder

[mmcirvin.livejournal.com]

I figured out how to do it:

..........OO
..........OO
............
O.....O.....
OOO.OOO.....
.O...O......

The asymmetrical perturbation also persists in B37/S23, making this a very dirty puffer/rake that produces chaos and streams of forward/diagonal gliders at various angles, which collide to produce unpredictable trails of junk. But the breeder behavior in B37/S238 is pretty spectacular.

Re: Smaller precursor to the B37/S238 breeder

[mmcirvin.livejournal.com]

...The boiling chaos around the departure point of this thing eventually shoots out a second breeder in the opposite direction. Also, a sideways puffer that travels in the space between two of the previously emitted puffer trails; there's somehow just enough room for it to get through halfway between, perturbing the trails on either side as it goes.

[doctroid.livejournal.com]

In B38/S2378 the pi heptomino

..o..
.o.o.
oo.oo

evolves into a chaotic space filler, a sort of 2-d replicator gone wrong that leaves seething randomness inside a quasi fractal boundary. Of course this arises naturally very easily and takes over any random soup, so the rule doesn't seem all that interesting, but I find this particular pattern attractive.

[mmcirvin.livejournal.com]

Actually that's quite nice; I don't think I'd investigated that particular rule before, having determined that adding 8 to the birth rule usually didn't cause obvious interesting differences. It's very in keeping with my theme here of "Life plus a rule that turns up the heat a little".

[mmcirvin.livejournal.com]

Now you've got me thinking about whether a stochastic mean-field approximation would accurately model the tendency of initial random soup in an outer totalistic CA to explode or not. By this, I mean modeling the time evolution of the average density of the soup assuming that every cell's neighbors are described by a Poisson distribution with the current density. "No" would be the most interesting answer, implying that the dynamics are dominated by specific quirks like initially small puffers and spacefillers.

I suspect somebody has already investigated this in detail, but all the likely papers are behind frickin' Elsevier's extortionate paywall.

[doctroid.livejournal.com]

Oh, wait, that's not a pi heptomino.

[mmcirvin.livejournal.com]

It might as well be one, though; I think the real pi does the same thing.

[ikkyu2.livejournal.com]

I had a cellular automata thingy on my Palm that I spent hundreds of hours fooling with during my residency when I couldn't sleep, so I know about the entertainment value. I was hoping that maybe smarter people were, you know, building rockets or viruses with cellular automata, or something along those lines.

[mmcirvin.livejournal.com]

I think Wolfram somehow uses a 1D CA to seed Mathematica's random number generator.

Know this one?

[doctroid.livejournal.com]

Seen puffer 1 in B37/S237?

Re: Know this one?

[doctroid.livejournal.com]

and in B378/S238

Re: Know this one?

[mmcirvin.livejournal.com]

Hmm, a puffer+rake and a block puffer, respectively.

I hadn't investigated those rules, got distracted by my ill-fated theoretical exercise instead.

Re: Know this one?

[mmcirvin.livejournal.com]

...Sadly, the perturbed version dies in both of them.

The pond puffer still does the same thing, though. It seems pretty robust across these variants.