Cellular automaton supercolliders

TL;DR

This paper investigates the interactions of gliders in one-dimensional cellular automata, demonstrating their collision behaviors and modeling computational processes through glider dynamics on a cyclic lattice.

Contribution

It provides a detailed analysis of glider interactions in cellular automata and models computational systems using glider collision dynamics.

Findings

Gliders exhibit fusion, elastic, and soliton-like collisions.

Collision behaviors emulate interactions in non-linear media.

Swarm dynamics can implement cyclic tag systems.

Abstract

Gliders in one-dimensional cellular automata are compact groups of non-quiescent and non-ether patterns (ether represents a periodic background) translating along automaton lattice. They are cellular-automaton analogous of localizations or quasi-local collective excitations travelling in a spatially extended non-linear medium. They can be considered as binary strings or symbols travelling along a one-dimensional ring, interacting with each other and changing their states, or symbolic values, as a result of interactions. We analyse what types of interaction occur between gliders travelling on a cellular automaton `cyclotron' and build a catalog of the most common reactions. We demonstrate that collisions between gliders emulate the basic types of interaction that occur between localizations in non-linear media: fusion, elastic collision, and soliton-like collision. Computational outcomes of a swarm of gliders circling on a one-dimensional torus are analysed via implementation of cyclic tag systems.