Notes

Chapter 3: The World of Simple Programs

Section 2: More Cellular Automata


Algebraic forms [for cellular automaton rules]

The rules here can be expressed in algebraic terms (see page 869) as follows:

• Rule 22: Mod[p + q + r + p q r, 2]

• Rule 60: Mod[p + q, 2]

• Rule 105: Mod[1 + p + q + r, 2]

• Rule 129: Mod[1 + p + q + r + p q + q r + p r, 2]

• Rule 150: Mod[p + q + r, 2]

• Rule 225: Mod[ 1 + p + q + r + q r, 2]

Note that rules 60, 105 and 150 are additive, like rule 90.

From Stephen Wolfram: A New Kind of Science [citation]