1-D Binary

From AoPSWiki

1-D Binary is a type of Cellular Automaton.

There are 256 rules, described as following in binary:

111,110,101,100,011,010,001,000

Where, for example, if bit 2 (110) is on, then if the previous generation's left bit and center bit are both on then the center bit for the next generation will also be on.

Each cell is affected by itself and its two neighbors in the previous generation.

An example: Rule 90 [01011010] (Sierpinski Triangle) This means: 001 -> 1, 011 -> 1, 100 -> 1, 110 -> 1 and 0 otherwise. Row1: 0000000000000000000100000000000000000000

Row2: 0000000000000000001010000000000000000000

Row3: 0000000000000000010001000000000000000000

Row4: 0000000000000000101010100000000000000000

Row5: 0000000000000001000000010000000000000000

Row6: 0000000000000010100000101000000000000000

Row7: 0000000000000100010001000100000000000000

Row8: 0000000000001010101010101010000000000000

And so on.

Rules of Interest

Rule 90 - This generates a Sierpinski Triangle.