Registered: Jul 2005
Posts: 7

I've continued working on a continuous model of the simplest cellular automaton.

First, I built a continuous mechanism that resembles the same patterns that a discrete one can do. The first iterations work good but sometimes noise appears in later generations so the patterns get altered but preserved.

I could also to parameterize this automaton in such a way that is posible to find a continuous straight path in the parameter space in order to transform patterns from a rule to another in a continuous fashion.

Adjoint I show some sequences that illustrate a transition from rule 30 to rule 110 patterns. It exhibits some abrupt jumps due to eventual entrances to chaotic regions that could be avoided by changing the parameter path.

What does this discovery mean?

In this parameter space is it posible to distinguish different zones that are associated to each one of the four classes of Wolfram's classificacion? and how common chaotic and complex behavior are?

Attachment: 30_110.zip
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Registered: Aug 2003
Posts: 712

Mixing CA Rules the ICA way

In the ICA set up, the rule to be applied at any given step of the evolution is determined by an external sequence. This creates a "machine with input" form of CellularAutomaton. By varying the sequence, one applies a different mix of the stated rules in some specific order. By altering the portion of the sequence with one value or another, one effectively mixes more or less of any given elementary rule, into the evolution of the ICA. The code provided is meant to take any number of ECA rules.

The attached notebook illustrates this idea. I'll provide jpgs for those without Mathematica, next.

Attachment: icarulemixer.nb
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Registered: Aug 2003
Posts: 712

And here are some simply JPGs made by the above notebook.

Attachment: icaillustrations.zip
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