Damage spreading and Lyapunov exponents in cellular automata

Using the concept of the Boolean derivative we study local damage spreading for one-dimensional elementary cellular automata and define their maximal Lyapunov exponent. A random matrix approximation describes quite well the behavior of “chaotic” cellular automata and predicts a directed percolation-type phase transition. After the introduction of a small amount of noise elementary cellular automata reveal the same type of transition.