Cellular Automata

This applet replicates an experiment in the field of cellular automata, as popularized in Stephen Wolphram's 2002 book, A New Kind of Science. It is an investigation of how simple algorythms can lead to complex behaviors. In this case, we are showcasing a procedure which asigns black or white values to cells in an array, according to a rule which the user can specify by toggling the boxes at the bottom of the applet. After starting with a single black cell at the top of the array, the procedure goes row by row through each cell and examines the values of the three cells in the row directly above it. By comparing these three values to the rule that was set by the user, it is determined whether a cell will be black or white. As this process continues throughout the array, various patterns emerge in the arrangment of the cells. Depending on the rule, these patterns can be regular and repititious, or structures that are random yet seemingly organized - bringing to mind some of the fractal demonstrations of chaos theory. As with chaos theory, the phenomona illustrated here have analogies and applications in the physical world, touching on such diverse fields as fluid dynamics, genetics, and nanotechnology. You are invited to toy with the applet above to discover for yourself this new kind of science.

How to Use the Applet

This applet draws a cellular automata based on a rule defined by the user. You can define the rule by clicking on the box groups at the bottom of the applet, to toggle them between producing a black cell or a white cell.

In the example above, the rule is defined so that any cell that has a black cell directly above and to the right of it, or directly above and to the left of it, will be a black cell, and all other cells will be white. This rule creates a simplest kind of nested triangle pattern. If you wish to zoom out on the pattern, to view it as a larger structure, you can do so by setting the "Cell Size" choice box to be a smaller value, before hitting the "Show Me" button.

Here are some other intersting examples of rules that you may want to try out. Look for recurring patterns as well as apparent randomness.

- Bobby Williams

Source Code of this applet.

Zip File of this package.