A ruleN pattern evolves down the image based on the previous line. They are numbered using the binary representation of N (in ruleN).
In the table below 1 = black and 0 = white. The result of the current pixel (bottom row) is defined by the 3 pixels in the row previous (top row).
Example: if the pixel has white/black/black above it this corresponds to 011, so the resulting pixel is the one below it.
See: for more.

 => 1101110 (these values are put into the below table for the result of the simulation)

(converted to binary, and placed on the top row of the image)  => 1
(can get slow on large numbers)
Double pixel size: 
Simulate or Random Start

It is possible to save the image this generates by right clicking on it.