Chaos in Binary Category Computation

Abstract

Category computation theory deals with a web-based systemic processing that underlies the morphic webs, which constitute the basis of categorial logical calculus. It is proven that, for these structures, algorithmically incompressible binary patterns can be morphically compressed, with respect to the local connectivities, in a binary morphic program. From the local connectivites, there emerges a global morphic connection that can be characterized by a low length binary string, leading to the identification of chaotic categorial dynamics, underlying the algorithmically random pattern. The work focuses on infinite binary chains of C2, which is a category that implements an X-OR-based categorial logical calculus.