Definite rules for rhythm in poetry were already well developed in antiquity—and by perhaps 200 BC Indian work on enumerating their possible forms appears to have led to both Pascal's triangle and Fibonacci numbers. … And in the past century a few composers have implicitly or explicitly used structures based on simple Fibonacci and other substitution systems.

The tree representation of rule (c) from page 83 was for example probably drawn by Leonardo Fibonacci in 1202.

Generalized Fibonacci generators. It was suggested in the late 1950s that the Fibonacci sequence f[n_] := f[n - 1] + f[n - 2] modulo 2 k might be used with different choices of f[0] and f[1] as a random number generator (see page 891 ).

. • 1200s: Fibonacci sequences, Pascal's triangle and other rule-based numerical constructions are studied, but are found to show only simple behavior. • 1500s: Leonardo da Vinci experiments with rules corresponding to simple geometrical constraints (see page 875 ), but finds only simple forms satisfying these constraints. • 1700s: Leonhard Euler and others compute continued fraction representations for numbers with simple formulas (see pages 143 and 915 ), noting regularity in some cases, but making no comment in other cases. • 1700s and 1800s: The digits of π and other transcendental numbers are seen to exhibit apparent randomness (see page 136 ), but the idea of thinking about this randomness as coming from the process of calculation does not arise. • 1800s: The distribution of primes is studied extensively—but mostly its regularities, rather than its irregularities, are considered.