# Cellular automaton supercolliders

@article{Martnez2011CellularAS, title={Cellular automaton supercolliders}, author={Genaro Ju{\'a}rez Mart{\'i}nez and Andrew I. Adamatzky and Christopher R. Stephens and Alejandro Frank Hoeflich}, journal={International Journal of Modern Physics C}, year={2011}, volume={22}, pages={419-439} }

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 traveling in a spatially extended nonlinear medium. They can be considered as binary strings or symbols traveling along a one-dimensional ring, interacting with each other and changing their states, or symbolic values, as a…

## Figures and Tables from this paper

## 31 Citations

### Computing on rings

- Computer Science
- 2012

The features of develop computations based on rings are reviewed and it is demonstrated 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.

### Computing with virtual cellular automata collider

- Computer Science2015 Science and Information Conference (SAI)
- 2015

Computer models of nano-scale computing circuits based on propagation of localised excitations or defects in complexes of polymer chain rings based on collisions that emulate basic types of interactions between localisations typical for spatially-extended non-linear media are presented.

### Self-Replicating Patterns in 2D Linear Cellular Automata

- Computer ScienceInt. J. Bifurc. Chaos
- 2014

The present work focuses on the theory of two-dimensional CA with respect to uniform periodic, adiabatic and reflexive boundary CA conditions and presents a successful application for generating pseudo numbers to be used in cryptography by hybridization of these 2D CA subfamilies.

### On Soliton Collisions between Localizations in Complex Elementary Cellular Automata: Rules 54 and 110 and Beyond

- Computer ScienceComplex Syst.
- 2012

A specific ECA with memory (ECAM), the ECAM Rule $\phi_{R9maj:4}$, that displays single-soliton solutions from any initial codification for a kind of mobile self-localization because such automaton is able to adjust any initial condition to soliton structures.

### 2D Triangular von Neumann Cellular Automata with Periodic Boundary

- Computer ScienceInt. J. Bifurc. Chaos
- 2019

The structure and the reversibility cases of two-dimensional (2D) finite, linear, and triangular von Neumann CA with periodic boundary case are investigated and the general transition rule matrices are presented to establish the reversible cases of these special 3-states CA.

### The Transition Rules of 2D Linear Cellular Automata Over Ternary Field and Self-Replicating Patterns

- Computer ScienceInt. J. Bifurc. Chaos
- 2015

This paper starts with two-dimensional (2D) linear cellular automata (CA) in relation with basic mathematical structure and investigates uniform linear 2D CA over ternary field, i.e. ℤ3 and deals with the theory 2D uniform periodic, adiabatic and reflexive boundary CA and the applications of image processing for patterns generation.

### Structure and Reversibility of 2D von Neumann Cellular Automata Over Triangular Lattice

- Computer ScienceInt. J. Bifurc. Chaos
- 2017

The structure and the reversibility of two-dimensional (2D) finite, linear, triangular von Neumann CA with null boundary case is investigated and it is believed that the present construction can be applied to many areas related to these CA using any other transition rules.

### Designing Complex Dynamics in Cellular Automata with Memory

- Computer ScienceInt. J. Bifurc. Chaos
- 2013

A systematic analysis displays that memory helps "discover" hidden information and behavior on trivial — uniform, periodic, and nontrivial — chaotic, complex — dynamical systems.

### Conservative Computing in a One-dimensional Cellular Automaton with Memory

- PhysicsJ. Cell. Autom.
- 2018

We propose a scheme to simulate Fredkin gates in a one-dimensional cellular automaton with memory by collision of particles, which is a moving pattern in this cellular space. Operations by collisions…

### A Computation in a Cellular Automaton Collider Rule 110

- Computer ScienceArXiv
- 2016

This work shows how a computation can be performed on the collider by exploiting interactions between gliders (particles, localisations) and proposes constructions based on universality of elementary cellular automaton rule 110, cyclic tag systems, supercolliders, and computing on rings.

## References

SHOWING 1-10 OF 70 REFERENCES

### Classifying Cellular Automata Automatically

- Computer Science
- 1998

The method allows screening out rules that display glider dynamics and related complex rules, giving an unlimited source for further study, and shows the distribution of rule classes in the rule-spaces of varying neighbourhood sizes.

### Particlelike structures and their interactions in spatiotemporal patterns generated by one-dimensional deterministic cellular-automaton rules.

- PhysicsPhysical review. A, Atomic, molecular, and optical physics
- 1991

A detailed description of such ``reactions'' sheds new light on the large-time behavior of range-1 Rule 54 with a very slow decrease of the particle number, as ${\mathit{t}}^{\mathrm{\ensuremath{-}}\ensure Math{\gamma}}$ (Â£0.15).

### Simulations of Mixtures of Two Boolean Cellular Automata Rules

- Computer ScienceComplex Syst.
- 1988

It is investigated if the Kauffman mod el is a phase tran sit ion as a function of the degree of mixing, par ticularly if one chooses one rule as forcing and t he other as non-forcing, and if there are quenched mixtures of two Boolean functi ons.

### On conservative and monotone one-dimensional cellular automata and their particle representation

- MathematicsTheor. Comput. Sci.
- 2004

### Universality in Elementary Cellular Automata

- Computer ScienceComplex Syst.
- 2004

The purpose of this paper is to prove that one of the simplest one dimensional cellular automata is computationally universal, implying that many questions concerning its behavior, such as whether a…

### Gliders, Collisions and Chaos of Cellular Automata Rule 62

- Physics2009 International Workshop on Chaos-Fractals Theories and Applications
- 2009

This paper provides a systematic analysis of glider dynamics and interactions in rule 62, including a catalog of glider collisions. Based on these empirical observations, it is proved that rule 62…

### Spatial updating, spatial transients, and regularities of a complex automaton with nonperiodic architecture.

- Computer ScienceChaos
- 2007

The spatial updating algorithm provides an alternative way to determine the dynamics of automata of arbitrary size, a way of taking into account the complexity of the connections in the lattice.

### One-dimensional Cellular Automata

- Computer Science

A lattice network of cells that are most commonly square in shape, but the cells can be hexagonal and other shapes as well, and one of these states has a special status and will be known as the ‘quiescent state’.