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3D Evolution of Colorized Morphological Components in 2D Totalistic Cellular Automata

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The left plot shows all evolution steps in the spacetime history of two-dimensional cellular automata (CAs) as one compact three-dimensional image. This is produced using the settings for "rule number," "initial condition" and "evolution step." The right plot shows a reverse version of the left from the same specifications. The time axes in both run from bottom to top.

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You can leaf through the three-dimensional spacetime diagrams in time. For example, setting "spacetime slice" equal to 1 gives the initial condition of the evolution history (left), with the latest evolution step shown in the reverse evolution history (right).

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Contributed by: Marius Bugl (August 25)
Open content licensed under CC BY-NC-SA

Details

Segmented components, as they arise, are colorized, based on their area and spread over the whole image, including each component in every layer. This applies to both images.

Subsequently, the resulting images (RGB, three channels, interleaved) can be copied and then pasted into an empty notebook for further treatment with Wolfram Mathematica's built-in image tool/clipping tool.

This Demonstration uses discrete two-state, range-one (nine-neighbor) totalistic 2D CAs. The largest possible rule number is 1023.

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