Chapter 7: Mechanisms in Programs and Nature

Section 9: Origins of Simple Behavior

Repetition in numbers

A common source of repetition in systems involving numbers is the almost trivial fact that in a sequence of successive integers there is a repetitive pattern of cases at which a particular divisor occurs. Other examples include the repetitive structure of digits in rational numbers (see page 138) and continued fraction terms in square roots (see page 144).

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