The Logistic Lattice in Random Number Generation

This paper describes pseudo-random number generators based on non-linear dynamics. The recommended generator uses a special “re-mapped” form of the logistic equation at each of a finite set of nodes arranged in a 1or 2-dimensional ring. Each node receives small perturbations from adjacent nodes by means of diffusive coupling equations the so-called coupled map lattice. The generator is notable as the first to use non-linear dynamics in a lattice with a continuous state at each node. Time and space are discrete, but the state is continuous, unlike the cellular automata that Wolfram used to produce random numbers. It is a new source of pseudo-random numbers, unlike other current sources. The paper gives evidence that this generator possesses good statistical properties and a very long period, except in cases of negligible probability.