Chapter 7: Mechanisms in Programs and Nature

Section 5: The Intrinsic Generation of Randomness

Probabilistic rules [for cellular automata]

There appears to be a discrete transition as a function of the size of the perturbations, similar to phase transitions seen in the phenomenon of directed percolation. Note that if one just uses the original cellular automata rules, then with any nonzero probability of reversing the colors of cells, the patterns will be essentially destroyed. With more complicated cellular automaton rules, one can get behavior closer to the continuous cellular automata shown here. (See also page 591.)

Image Source Notebooks:

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