Registered: Feb 2004
Posts: 35

I've found an interesting connection between the symmetrical rules 110/124 and 30/86. There are other rules that connects these two pairs, so I went back to this ICA and added these rules. The result is similar, but the randomness eventually dies off after doing some interesting branching.

I've attached a 4800 step example starting from random initial condition.

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Last edited by Alastair Hewitt on 09-07-2005 at 03:42 PM

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Registered: Aug 2003
Posts: 712

Those are nice. One might make an exhaustive survey of symmetric ICAs, not just ones based on the "famous" rules.

I've added such a survey of symmetric rule ICAs to the attached notebook. All the pairs are given and typical behavior of their ICA mixes from simple and random initial conditions are shown.

The next step would be to look for combinations of initial conditions and interaction sequences that give relatively rare, interesting behavior.

Attachment: icarulemixsym.nb
This has been downloaded 1308 time(s).

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Registered: Feb 2004
Posts: 35

I've looked at a lot of ICA combinations with 110/124 and 30/86. I originally found combinations of "124 30 110 86" and it's mirror "110 86 124 30" gave interesting patterns when 2 and 2 of these four rule sequences were repeated and 5 and 5.

I also had a look at how to transpose the bits of rule 30 to get to rule 86, and 86 to 30. If you do the transposition the other way (the 30->86, applied to 86), you end up with rule 54. Doing the same for 110/124 gives you rule 122. With the intermediate rules 54 and 122, I came up with these two mirrored sequences:

122 86 54 124
122 30 54 110

The example above was "2 and 2". and I've attached the "5 and 5" below. This one dies off a lot faster, but ends in a more consistent pattern.

It's also fun to combine 54 and 122 on their own. It's gives what looks like a class 2 at first, but it progresses with a random sequence of large central triangles

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Registered: Feb 2004
Posts: 35

Attached is another example of the "5 and 5" ICA from above. I ran a lots of random initial conditions into it and got one with a pair of "streamers" approaching almost 2000 steps in length.

In order to compress the image, I skip alternate rows and columns, so it looks a bit different. I've cropped this one and have it as desktop wall paper (1280x1024).

Enjoy!

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