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A cellular automaton (plural: cellular automata) is a discrete model studied in computability theory, mathematics, and theoretical biology. It consists of an infinite, regular grid of cells, each in one of a finite number of states. The grid can be in any finite number of dimensions. Time is also discrete, and the state of a cell at time t is a function of the states of a finite number of cells (called its neighborhood) at time t-1. These neighbors are a selection of cells relative to the specified cell, and do not change. (Though the cell itself may be in its neighborhood, it is not usually considered a neighbor.) Every cell has the same rule for updating, based on the values in this neighbourhood. Each time the rules are applied to the whole grid a new generation is produced.

Overview


One example of a cellular automaton (CA) would be an infinite sheet of graph paper, where each square is a cell, each cell has two possible states (black and white), and the neighbors of a cell are the 8 squares touching it. Then, there are 29 = 512 possible patterns for a cell and its neighbors. The rule for the cellular automaton could be given as a table. For each of the 512 possible patterns, the table would state whether the center cell will be black or white on the next time step. This is an example of a two dimensional cellular automaton. See Conway's Game of Life for the most popular CA of this form.

It is usually assumed that every cell in the universe starts in the same state, except for a finite number of cells in other states, often called a configuration. More generally, it is sometimes assumed that the universe starts out covered with a periodic pattern, and only a finite number of cells violate that pattern. The latter assumption is common in one-dimensional cellular automata.

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Meta Description: [ Cafun is a powerful and easy application to create impressive simulations of complex systems. ]

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Cellular Automata Laboratory - An extendable DOS/Windows application for exploring cellular automata, accompanied by a thorough user guide; by Rudy Rucker and John Walker.

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Meta Description: [ Pioneered by scientist Edward Fredkin, Digital Physics is a study of physics as a digital phenomenon. ]

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Meta Description: [ Windows software for exploring five cellular automata: q-state Life (a generalization of Conway's Life), the Belousv-Zhabotinsky Reaction, Togetherness, Viral Replication and Diffusion-Limited Aggregation. ]

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Meta Description: [ MetaCrawler Metasearch. ]

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Meta Description: [ NetPlay Software - taking chaos to the limit... ]

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Meta Description: [ Software Download Page ]

Hexatron - A Java demonstration of cellular automata on a hexagonal grid.

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Introduction to Cellular automata - (game of life, brian's brain...) available in PDF, illustrated with a program (CAV) and an applet which show the capability of a conway CA to manage boolean functions as part of a Turing machine(LogiCell).
Meta Description: [ Introduction to cellular automata illustrated by two programs. The text is available in PDF. ]

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Java applets collection - Links to sites containing applets for various CA: Conway's game of life, Bays' 3-D life, triangular CA and life objects, and some new games of life that have been discovered in the hexagonal and pentagonal tessellations.

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Meta Description: [ artificial life research ]

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Meta Description: [ Texture Garden, for growing algorithmic textures. ]

Mirek's Cellebration - 1D and 2D Cellular Automata viewer, explorer and editor by Mirek Wojtowicz. Huge libraries of CA rules and patterns, gallery of CA rules, news, links. Free 32-bit Windows MCell software.
Meta Description: [ Mirek's Free Software: Cellular Automata, Windows and Palm freeware ]

Mirek's Java Cellebration - General Cellular Automata Java applet running over 200 rules from 12 CA families, equipped with a big library of patterns. By Mirek Wojtowicz.
Meta Description: [ 1D and 2D Cellular Automata Java applet ]

Modern Cellular Automata - Color cellular automata for the World Wide Web, by George Maydwell.
Meta Description: [ Java powered plethora of live color cellular automata with traditional, fractal, pattern, and unique hexagonal cellular automata. Fast free software. ]

Moshe Sipper's Home Page - Fine theoretical and practical introduction to Cellular Automata, ALife, and Complex Adaptive Systems.
Meta Description: [ Web Site of Moshe Sipper ]

SARCASim - Home Page of SARCASim (Super Animation-Reduction CA Simulator) and ARCAL language, by George Maydwell.
Meta Description: [ George Maydwell's Cellular Automata Page, the home page for SARCASim. ]

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404 Searching for Chaos in Cellular Automata - New tools for CA classification by Paola Flocchini and Frédéric Geurts
Meta Description: [ Charles Sturt University (CSU) located in the cities of Albury-Wodonga,Bathurst and Wagga Wagga, three of the fastest growing cities in NSW. As well as these campuses, the University is represented in places as diverse as Dubbo, Manly, Goulburn, Broken Hill, Canberra and the central business dist... ]

Self Reproducing Cellular Automata Loops - Christopher Osborn's Java applet exploring self-reproducing patterns.
Meta Description: [ Cellular Automata application with rules exploring self reproducing patterns. ]

Stephen Wolfram's articles on Cellular Automata - Technical articles by one of the leading CA researchers, concerning both 1D and 2D Cellular Automata.

Stone's Free Mac Programs - Many free CA, ALife, and Chaos programs for Macs.

404 The CA Extension - An implementation of cellular automata for the GIS software ArcView from ESRI.

The Primordial Soup Kitchen - Colorful images and Java movies of Cellular Automata, with recipes to explain their genesis. Also some tasty Real Recipes. By David Griffeath.
Meta Description: [ Colorful images and Java movies of cellular automata, with recipes to explain their genesis. Also some tasty Real Recipes. ]

Universal Cellular Automaton - A Java Applet for simulating all kind of cellular automata, including Conway's Game Of Life or snowflake generation rules. By Frank Buß.

Visions of Chaos - Home page of a versatile Windows software by Jason Rampe. The program covers Cellular Automata, Chaos, and Fractals.
Meta Description: [ Visions Of Chaos ]

XToys - A set of Cellular Automata simulators written for XWindows. By Mike Creutz.

ZenStrings - An algorithmic music entity that creates evolving musical textures based upon initial parameters determined by its human composer; by Gary Bourgeois.

Zooland - A big (200+) collection of resources for those interested in studying Artificial Life and Cellular Automata.

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