Registered: Jan 2004
Posts: 351

Attached is the graphic for an interesting cellular automaton. It begins with a simple nested behavior that is diamond shaped. But then there occurs a more complicated structure. Down the center it has a definite and endlessly varying symmetric structure. However, as the cells spread out away from this center they have a pattern-free, random appearance. Actually, the pattern-free appearance on the right side is a reflection of that on the left side. So, even though our perceptive powers cannot recognize it, the entire cellular automaton — after the nested diamond shape — is an example of random symmetric behavior.

Is this a new kind of cellular automaton? The closest approximation to this cellular automaton in the NKS book seems to be the borderline cases discussed on page 240. But the borderline cases mix the characteristics of one or more classes horizontally while this cellular automaton has a clear demarcation between the simple nested structure and the random symmetric structure. And the simple nested structure terminates early while the random symmetric structure goes on indefinitely. If it is new, perhaps it might be called a hybrid.

This is an example of a ten color cellular automaton that updates its cells by taking the modulo ten sum of the cell and its two adjacent neighbors. It uses this sum as a pointer to locate the update value of the cell from the rule which is a list of ten base ten integers: {39, 29, 49, 16, 36, 65, 57, 0, 95, 26}. The initial conditions for this example were a row of zero value cells with a single one value cell at the center. The graphic represents 2500 steps with a width of 2047 cells. I have run the cellular automaton for 10,000 steps without finding any repetition in the random symmetric behavior.

Lawrence J. Thaden has attached this image:

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L. J. Thaden

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