Table 4: Difference Patterns

Differences in patterns produced by evolution from disordered states resulting from changes in single initial site values.

The evolution of small perturbations made in the initial configurations for all the ``minimal representative'' rules of table 1 are given. In each case, an initial configuration was chosen in which sites had value 0 or 1 with probability , and the pattern obtained by evolution according to the cellular automaton rule was found. Then the value of the centre site in the initial configuration was complemented, and the resulting pattern obtained by cellular automaton evolution was found. The pictures show as black squares the site values that differed between the patterns found with these initial configurations. Evolution for 40 time steps is shown.

In some cases, the differences die out, or remain localized, with time. In other cases, the differences grow. The left and right growth speeds correspond to the left and right Lyapunov exponents and , given in table 6.

For some rules (such as 18), initial perturbations on some configurations may grow, but on others may die out. The pictures show results from a particular trial.

previous  l  next