Complex Systems

Cellular Automata Complexity Threshold and Classification: A Geometric Perspective Download PDF

Mohamed Al-Emam
Cairo University
Faculty of Engineering, Electronics, and Communications Department
Giza, Cairo, Egypt
emamof@gmail.com

Vitaliy Kaurov
Wolfram Research, Inc.
100 Trade Center Drive
Champaign, IL 61820

Abstract

This paper presents the results of mathematical experiments on the so-called "orientation vector." It looks at complexity in terms of three perspectives: Wolfram, Langton, and Chua. Critically, we consider Chua's geometrical complexity index and a complexity-based classification of elementary cellular automata. Ideas in terms of solutions for ordinary differential equations and complexity measurements are proposed to the research community for discussion.