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2D Pattern forming Cellular Automata

 

Two Dimensional Pattern Forming CA

You can view the source code here

Pigmentation Patterns in Biological Systems Objective : Develop a Java applet which can generate patterns similar to biological pigmentation patterns. Methodology: The applet is based on 2D cellular automata which will use the Manhattan distance from the cell and an associated weight in determining the contents of a single cell. Each cell is assigned an associated weight based on the distance to it. Therefore the system has a certain radius attached to each weight. The following image displays one possible configuration for the system, where 4 different weights are assigned to cells with distance 0,1,2 and 3 from the primary cell.   It is also possible to assign the same weight to cells of different distances, such a scenario is shown below:

The applet can be improved (as suggested by Wolfram), by using 2 sets of distance measurements (vertical and horizontal) with two sets of weights. This it is hypothesized would make it possible to generate vertical or horizontal stripes as patterns. Whether the neighborhood of a a cell has edges or not is not clear in Wolfram's details regarding the implementation. One possible improvement is to allow the user to select the type of neighborhood from a selected set of patterns such as shown below: