Chapter 2: The Crucial Experiment

Section 1: How Do Simple Programs Behave?

[Patterns from] other integer functions

[Patterns from] other integer functions image 1

The pictures above show patterns produced by reducing several integer functions modulo 2. With d arguments Multinomial yields a nested pattern in d dimensions. Note that GCD[m, n] yields a more complicated pattern (see page 613), as do JacobiSymbol[m, 2n - 1] (see page 1081) and various combinations of functions (see page 747).

Image Source Notebooks:

  • Wolfram Language source code for image on page 870

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