Condensed Cellular Automaton States

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States of elementary cellular automata with periodic boundary conditions and periodic binary numbers in general can be visualized by picking either ones or zeros from n overlapping disks on the unit circle. Those areas covered by an odd number of selected disks are marked.

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This Demonstration shows the evolutions of initial conditions with 12 bits. Enable color encoding to identify the 4096 possible 12-bit states with 4-bit intensities of red, green, and blue channels. The overlapping disks cover range-1 neighborhoods to group each value with its two neighbors. Periodic repetitions of images and similar colors indicate that the evolution has entered a map orbit.

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Contributed by: Michael Schreiber (March 2011)
Open content licensed under CC BY-NC-SA


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