Registered: Nov 2011
Posts: 4

Since the Summer School, I've been searching for slow growing chaotic CAs in the k=2, r=2 ruleset. Thus far, I've been focusing on a portion of the ruleset that I identified as having a large proportion of slow growing CAs, which has yielded some interesting results. The slowest class 3/4 I've found so far is only 41,423 cells wide after one million steps. I'm working on refining my searching methods in order to do an exhaustive search of the entire rulespace.

I noticed that Stephen did a live experiment ~6 years ago that touched on this problem:

http://forum.wolframscience.com/sho...hp?threadid=753

I didn't find find anything else posted on the forum on this topic, does anyone know if someone else has followed up on this question?

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Registered: Sep 2011
Posts: 4

Interesting topic.

does the growth appear to be linear, or can it slow down?

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Registered: Nov 2011
Posts: 4

It's irregular, but overall it's linear.

I've attached a plot of the growth rate over the first 200,000 steps and some images of the evolution.

Attachment: 31073675.zip
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Registered: Oct 2003
Posts: 103

Incredible rule. Definitely a live one.

I see it comes close to dying out, is it actually possible?

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Registered: Nov 2011
Posts: 4

Hard to say for sure. There are a number of points where it's barely updating any cells at all, [1] and it's not hard to find local branches, even large complex ones, that resolve to repeating patterns absent any interaction with the larger plot. [2] On the other hand, after 13,000 steps the number of cells updated at any given step doesn't seem to drop below a couple dozen.[3]

On the third hand, I found a CA that exhibits complex transient behavior for ~32,000 steps before settling down, [4] so there's a good chance that there's no way to know without running it.

1. DifferencePattern.png

2. DeadBranches.png

3. UpdatedCells.png

4. Rule 670738548

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Registered: Nov 2011
Posts: 4

Meant to attach this:

Attachment: 670738548.zip
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