Fractal cellular automata

[TGlad]

Hello all,
here is a video of variations of a fractal cellular automata. In addition to the translation symmetry of usual cellular automata they also have scale symmetry:

http://vimeo.com/36816056

Let me know if you like them. They all use the same algorithm, just varying the mapping tables.

[Pilou]

Seems like fluids simulation

[Hektor]

Seems really interesting, is there any program to run these Automata?

[TGlad]

Yes, I wrote the program, here it is: https://docs.google.com/open?id=0B8S7Si ... U3OTMyZmNm
I didn't have time for a GUI, so the control keys are described in the command window. Let me know if you have problems.

Since the number of possible mappings is huge, the program lets you search for a result by picking and mutating.
All the systems start off from a random set of bits, and the interesting ones self-organise into something.

You can load and save results, and I have included a few examples.

Here's a little bacteria using a very simple mapping based on the number of neighbours:

http://vimeo.com/36867848

[TGlad]

And two more petri dish specimens, hi res: http://vimeo.com/36951270

[Tropylium]

How exactly does scale symmetry go in hand with the discreteness of normal cellular automata? I'm assuming there's a maximum scale, and further detail is added by breaking cells down into smaller ones, but how does this work when eg. a large-scale cell is supposed to survive, but its constituents at a smaller scale evolve into a spark?

[TGlad]

I think it depends on the mapping, but the interesting mappings (that don't look like white noise) seem to sort of self-organise, so the low-res scales more or less match the high-res scales.
So if the smaller scale evolves into a spark and disappears this may encourage the large scale cell to disappear, equally, if the large scale remains this may encourage the smaller scale cell not to disappear.
In the app, the small square to the right of the centre top square is the next scale up from the centre top square, so you can see how it evolves alongside, if you load one of the examples.

[TGlad]

... I have added a sixth type, which only operates on the parent cells, so doesn't animate.
The tool is presented now on this page: https://sites.google.com/site/tomlowepr ... mataFinder
where you can download it. It now starts up with six examples.