In process of development.

Picture a fine grid of squares where each square is painted either black or white. In the first line of squares, randomly select which squares are to be painted black. Then develop a set of rules that determine the color of each square in the next line of squares based on the color of the three nearest neighbors in the previous line. For example, a square in the second line is to be painted white if all three of its previous neighbors are black. Or, the square is to be painted black if only the immediately previous square in the previous line is black. Etc. Based on this model, there are 256 rule sets from which to choose the rule set that will be run for a given iteration. The model graphically portrays the evolution the CA based on a random selection of black cells in the first row and the use of a given rule set.

The following figure contains both a graphical representation of eight rules for coloring a cell and a grid containing rows of 11 cells each. The first row of cells contains black squares whose number and positions are randomly generated. In this case, there are black cells placed in columns 4, 7, and 10. The rule set defines the color of each cell in the next row based upon the colors of the three nearest neighbors in the previous row. For example, the first (leftmost) rule says "if all three of my previous nearest neighbors are black, color me white". The sixth rule says "if my nearest neighbor immediately above me is black and my two diagonally positioned nearest previous neighbors are white, color me black".

This process of evolving a pattern from complex (random) initial conditions on the first line of cells and a simple set of rules results in an endless array of pattern structures.

This document is a draft of work in progress. Please post your comments, thoughts, and suggestions:

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