Chapter 7: Mechanisms in Programs and Nature

Section 4: Chaos Theory and Randomness from Initial Conditions


A somewhat related system is formed by a billiard ball bouncing around on a table. The issue of which sequence of horizontal and vertical sides the ball hits depends on the exact slope with which the ball is started (in the picture below it is 1/2). In general, it is given by the successive terms in the continued fraction form (see page 914) of this slope, and is related to substitution systems (see page 903). (See also page 1022.)

Image Source Notebooks:

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