About a Discrete Cellular Soliton (computer simulation)

TL;DR

This paper introduces a novel reversible cellular automaton with unique properties like rapid state recurrence, numerous conservation laws, and paradoxical symmetries, expanding understanding of complex discrete dynamical systems.

Contribution

It presents the first mathematical model of a reversible cellular automaton exhibiting paradoxical symmetries and conservation laws, with potential implications for complex systems analysis.

Findings

Frequent quick return to initial states

Presence of many conservation laws

Existence of paradoxical 'fuzzy' symmetries

Abstract

For the first time a mathematical object is presented - a reversible cellular Automaton - with many paradoxical qualities, the main ones among them are: a frequent quickly return to its original state, the presence of a large number of conservation laws and paradoxical "fuzzy" symmetries, which connects the current position of the automaton with its signature Main Integral.