Chapter 9: Fundamental Physics

Section 4: Conserved Quantities and Continuum Phenomena

Block rules [examples]

These pictures show the behavior of rule (c) starting from some special initial conditions.

The repetition period with a total of n cells can be 3^n steps. With random initial conditions, the period is typically up to about 3^n/2. Starting with a block of q black cells, the period can get close to this. For n=20, q=17, for example, it is 31,300.

Note that even in rule (b) wraparound phenomena can lead to repetition periods that increase rapidly with n (e.g. 4820 for n=20, q=15), but presumably not exponentially.

In rule (d), the repetition periods can typically be larger than in rule (c): e.g. 803,780 for n=20, q=13.

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