The above picture shows a cellular automaton working on an array 1000 cells with each iteration drawn below each other. The rule of this particular automaton is easy to describe when using a graphical notation:

The value of the next generation cell depends on the value itself and its two neighbours. Wolfram lists all these combinations and numbers them from right to left with 0-7 which then names the automaton by taking these 0's and 1's as binary number. The automaton in this example shows therefore rule #18.

After reading A New Kind of Science written by Stephen Wolfram I wanted to draw these pretty pictures myself. So I wrote up a little, slow and inefficient implementation in chicken scheme that drew all the pictures in this post. Drawing is done with the ezxdisp egg. You can have a look at the scheme source here.

A rule 39 CA.

A rule 182 CA.