Chapter 12: The Principle of Computational Equivalence

Section 10: Intelligence in the Universe

Properties [of doubling rules]

The number of steps increases irregularly but roughly quadratically with n in rule (a), and roughly linearly in (d) and (e). Rule (b) in the end repeats every 128 steps. The center of the complex pattern in both (d) and (e) emulates k = 2 rule 90.

Image Source Notebooks:

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