Parallel Computation Using Generalized Models of Exactly Solvable Chaos

Abstract

How chaos is useful in the brain information processing is greatly unknown. Here, we show that the statistical property of chaos such as invariant measures naturally organized under a great number of iterations of chaotic mappings can be used for some complex computations, while the precise information of initial conditions which vanishes in the course of iterations deos not matter for this kind of computations. The key observation of the present study is that computation using ergordicity of dynamical systems can be thought of as massively parallel Monte Carlo simulations. Here, to avoid difficulty in elucidating the ergordicity of dynamical systems, we propose computational schemes using the generalized class of one-dimensional chaos with explicit invariant measures. The validity of our results which connect chaos with parallel computation is checked by the precision computations of some transcendental numbers like π.