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I'm working on making patterns for a digital lava lamp (essentially, making interesting patterns using a 4x10 grid), and I've been looking into cellular automata. I tried implementing some variations on Langton's Ant but it tends to loop in very boring ways. Does anyone have any suggestions for interesting automata on small boards?

The lamp I'm working on can be played with here.

Any suggestions on a more appropriate place to post this question are welcome.

EDIT: By interesting, I mean patterns that work well on small boards. For example, Langton's Ant was not interesting because it always tended to find some static state over such a small board.

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  • $\begingroup$ Are you familiar with reaction-diffusion systems? Something like the B-Z reaction ( en.wikipedia.org/wiki/Belousov%E2%80%93Zhabotinsky_reaction ) might be a good automaton-like approach for pattern-making... $\endgroup$
    – Steven Stadnicki
    Commented Apr 10, 2014 at 21:55
  • $\begingroup$ What is "interesting" for you? $\endgroup$
    – Raphael
    Commented Apr 11, 2014 at 6:32
  • $\begingroup$ @StevenStadnicki That looks both like it would be awesome and very difficult to model...I'll give it a try on Monday. $\endgroup$
    – progressiveCavemen
    Commented Apr 12, 2014 at 20:49

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"interesting" is very subjective.

You could try Brian's Brain or Brian's Seeds, both of which I find interesting.
http://en.wikipedia.org/wiki/Seeds_%28cellular_automaton%29

While they are designed for an infinite plane, you could wrap your 4x10 grid at the top and bottom presenting a theoretical sphere instead of a plane.

As a interesting thought, you could start with Langton's ant and then add a swarm to the ant, then chose a random element of the swarm to take over control for the next X iterations.

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  • $\begingroup$ I looked into Brian's Brain and some other variations, but they seemed to require a decently large space to really do what they do. Since looping the grid changes the expansion, it seems like it will need a different type of automaton. I may still try Brian's Brain (Implementing different rules is the easy part anyway) $\endgroup$
    – progressiveCavemen
    Commented Apr 12, 2014 at 20:47
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The smallest "interesting" cellular automaton I know of is an ant that counts in binary. It's the same as Langton's Ant, except where Langton's Ant turns to the right on a black (or lit) square, this one doesn't turn and just continues forward. (On a white/unlit square, it still turns to the left like Langton's does.)

(Its rule is RN in the "multi-color ant" naming scheme, or 120010 in the "multi-state ant" or general "turmite" naming scheme.)

It counts in single pixels, but is symmetrical around both axes, so it will use 2x10 pixels to count in 5 bits (from 0 to 31).

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