[Images in CAs] - A New Kind of Science: The NKS ForumA New Kind of Science: The NKS Forum
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Images in CAs
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Posted by: Lawrence J. Thaden
Some like to imagine they see images in clouds. Here is a CA for them. I call it totem3000, because it reminds me of the figures that might be carved onto a totem pole, and because it is the result of rule 3000 out of a system of about 20,000 rules.
This system consists of algebraic expressions in four variables (p, q, r, s) each constrained to three possible values (0, 1, 2). The particular algebraic expression used here is: Rule 3000: Mod[ p – pr + s + qs, 3].
The apparent symmetry is a result of engineering the following pattern into the initial conditions. The left half has a 1 wherever the reverse of the right half has a 2 and visa versa. Also, wherever there is a zero on one side, it is also in the corresponding location on the reverse of the other side.
Here is the set of initial conditions:
Left half: 0,2,0,1,0,2,0,1,0,0,2,0,0,0,0,2,2,0,
Right half reversed: 0,1,0,2,0,1,0,2,0,0,1,0,0,0,0,1,1,0
The number at the foot of each column is the step reached at the bottom of the column. The first 2130 steps occur before a loop of 18 steps begins. So the last two steps are a beginning of the second instance of the loop.
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