On The Dynamical Nature Of Computation

TL;DR

This paper explores the chaotic and fractal nature of computation, showing that non-terminating processes are almost surely chaotic and autonomous learning identifies fractal sets, extending dynamical systems theory to computation.

Contribution

It introduces a novel perspective on computation as a dynamical system, applying chaos theory and fractal analysis to non-continuous fixed point iterations.

Findings

Non-terminating computation is almost surely chaotic.

Autonomous learning almost surely identifies fractal sets.

Standard chaos notions are extended to computational processes.

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.