CELLULAR AUTOMATA

Let us make a row of 5 cells and fill it with binary numbers as in figure 1. Only the center cell contains "1" and all other cells have "0s".
Now let us frame one rule and start a game.

Rule: "If either one of a cell's neighbors are 1, but not both, then the corresponding cell the next row will get 1 otherwise it will have 0".
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Refer figure 2. First cell do not have neighbors of 1, so first cell in the second row get 0. Second cell's right neighbour is 1. Hence the corresponding cell in the second row gets 1. Proceeding with the rule, we can fill up the second row.

Apply the rule and create up to 4 rows. Blacken the cells having 1 and leave the cells with 0s blank.
So a pattern is starting to emerge.(figure 3&4)

If we add more rows and more cells( a computer program is suitable), the pattern as given in the figure 5 appears. Oh, it is sierpinski triangles, a fractal. This process is cellular automation.

This process is used in image processing. For example, to convert a photo in gray scale to black and white document. It is also used in cryptography and in error correcting code. Try to make your own rules and create a game.

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