On The Dynamical Nature Of Computation

Abstract

Dynamical Systems theory generally deals with fixed point iterations of continuous functions. Computation by Turing machine although is a fixed point iteration but is not continuous. This specific category of fixed point iterations can only be studied using their orbits. Therefore the standard notion of chaos is not immediately applicable. However, when a suitable definition is used, it is found that the notion of chaos and fractal sets exists even in computation. It is found that a non terminating Computation will be almost surely chaotic, and autonomous learning will almost surely identify fractal only sets.