Mathematics · Study 050
Rule Scarf
One-dimensional cellular automata knit an endless scarf row by row, switching between Rule 30, 90, 110 and nine other famous rules.
What you're looking at
Each row is a line of on and off cells. A cell's state in the next row depends only on itself and its two neighbours, and there are 256 possible lookup tables for that, numbered 0 to 255. Each rule begins from a single on cell and is knitted for a while before the next one takes over.
The idea behind it
Stephen Wolfram catalogued these rules in the 1980s. Rule 90 draws the Sierpinski triangle. Rule 30 is chaotic enough to have been used as a random number generator. Rule 110 was proved in 2004 to be capable of universal computation, which makes it about the simplest known system that can compute anything.
Try this
Click or tap to cast on the next rule immediately.
