Chapter 6: Starting from Randomness

Section 5: Randomness in Class 3 Systems

Rule 225 [with simple initial conditions]

With initial conditions consisting of a single black cell, this class 3 rule yields a regular nested pattern, as shown on page 58. But with the initial condition , it yields the much more complicated pattern shown below. With a background consisting of repetitions of the block , insertion of a single initial white cell yields a largely random pattern that expands by one cell per step. Rule 225 can be expressed as Xor[Not[p], Or[q, r]].

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