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Lawrence J. Thaden


Registered: Jan 2004
Posts: 356

Elementary 4 Color Modulistic Cellular Automata

In the attached graphic is the set of 256 elementary 4 color modulistic cellular automata. They were run for 256 steps and had the same initial conditions: a row of 511 cells with zero values in all except the center cell which was 1.

These cellular automata update their cell values with one of the digits of their rule by summing the previous cell and its right and left neighbors modulo 4. The modulo 4 result is a pointer into the list of digits in the rule numbered from right to left starting with zero.

The behavior of these cellular automata can be described by inspecting the features of their graphs. (In what follows the numbers in parentheses are examples of rules which illustrate the described feature. Please refer to the attached graphic to see a rule and its behavior.)

All of the graphs are symmetrical.

All of the graphs have either a solid background (15) or a horizontally striped background (10).

When they also have a foreground, it falls into one of two shapes: vertical (60) or triangular (116).

The vertical shapes are either centered and linear (1), or within a triangle (41).

When linear, they are either a straight line (105) or a more complex shape (227).

When they are more complex, they are either repetitive (121) or non-repetitive, irregular shapes (158).

When they are triangular shapes, they are either right triangles (148) or acute triangles (193).

The right triangles may have their interior filled with a solid (84), a linear, vertical shape (61), multiple parallel vertical structures (152), nested structures, both simple and complex (100), or random textured objects (135).

The acute triangles all have random textured objects (242).

The random textured objects have local structures that are either clearly delineated (82), or more obscure (210).

Lawrence J. Thaden has attached this image:

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