Chapter 6: Starting from Randomness

Section 7: The Notion of Attractors

Iterated maps

For maps of the form x a x (1 - x) discussed on page 920 the attractor for small a is a fixed point, then a period 2 limit cycle, then period 4, 8, 16, etc. There is an accumulation of limit cycles at a ≃ 3.569946 where the system has a special nested structure. (See pages 920 and 955.)

Image Source Notebooks:

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