Chapter 6: Starting from Randomness

Section 5: Randomness in Class 3 Systems

Density in rule 90

From the superposition principle above and the number of black cells at step t in a pattern starting from a single black cell (see page 870) one can compute the density after t steps in the evolution of rule 90 with initial conditions of density p to be (see also page 602)

1/2 (1 - (1 - 2 p)^(2^DigitCount[t,2,1]))

Image Source Notebooks:

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