A study of Inverse Ultra-discretization of cellular automata
Norihito Toyota
TL;DR
This paper introduces a systematic inverse ultra-discretization method for cellular automata, deriving difference equations for all elementary cellular automata and demonstrating their behaviors through numerical solutions.
Contribution
It presents a novel systematic approach to inverse ultra-discretization of cellular automata using a functionally complete operation, deriving equations for all ECAs.
Findings
Difference equations successfully reproduce ECA behaviors
Method applies to all 256 elementary cellular automata
Numerical solutions validate the approach
Abstract
In this article, I propose a systematic method for the inverse ultra-discretization of cell automata using a functionally complete operation. We derive difference equations for the 256 kinds of elementary cellular automata(ECA) introduced Wolfram\cite{wolfram} by the proposed means of the inverse ultra-discretization. We show that the behaviors of ECAs can be completely reproduced by numerically solving the obtained difference equations.
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Taxonomy
TopicsCellular Automata and Applications · Advanced Materials and Mechanics · Semiconductor Quantum Structures and Devices