Introducing cellular automata
This project is inspired by Stephen Wolfram's book "A New Kind of Science". The book is rich with images demonstrating what the author views as a window to re-thinking the possibilities of scientific procedure.
This page provides a brief introduction on how cellular automata are created.
How the image is constructed
Cellular Automata are grid based formations defined by a "Rule" that determines the identity of each element. While it is entirely possible to generate Cellular Automata manually using tools as simple as a pencil and graph paper, a computer can produce them far more efficiently. In the examples that follow, a formation will be be produced in an operation similar to placing rows of tiles in a pattern.
In this example the first row drawn is predefined to have a single blue square in the center. The row length is a variable, here it's 9. In the rows that follow, the identity of each component, whether blue or white, will be determined by the identity of the three components in the row immediately above it.
To begin the next row the computer now chooses the color of the first open cell (marked with an X), by checking the color of the 3 cells immediately above it, above-left, and above-right.
*(Because of my deficiencies as a programmer, the first and last cells of each row are always white. This is an error with respect to producing accurate sets as in the Wolfram book, however, this method produces some interesting variations.)
Rule
The Rule for this situation specifies blue if the upper 3 are white, so the cell marked "X" will become blue.
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| Finished |
Since our Rule allows no option other than blue for any situation, all the remaining cells in row 2 will be blue as well. If we were to create a third row it would be identical to the second row. Things get more interesting once you start changing the Rule to make white an option.
Binary Numbers
The state of the Rule can be expressed as a binary number. If we let blue be represented by 0, and white by 1, the Rule as show above would produce the binary number 00000000, which is equivalent to the more familiar decimal number 0.
Rule for decimal number: 0, binary number: 00000000
Rule for decimal number: 1, binary number: 00000001
This simple set of conditions yields 255 possible combinations. Incredibly, a small percentage produce a chaotic result. One wouldn't think that possible from an operation so similar to throwing dice, but it is, and offers a tiny and very simplified model of how the world unfolds. Please refer to the Wolfram book for a sophisticated analysis of this idea.
Explore
Please click this link to create formations on your own. 
