Notes

Chapter 6: Starting from Randomness

Section 3: Sensitivity to Initial Conditions


Lyapunov exponents

If one thinks of cells to the right of a point in a 1D cellular automaton as being like digits in a real number, then linear growth in the region of differences associated with a change further to the right is analogous to the exponentially sensitive dependence on initial conditions shown on page 155. The speed at which the region of differences expands in the cellular automaton can thus be thought of as giving a Lyapunov exponent (see page 921) that characterizes instability in the system.


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