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         Cellular Automata:     more books (100)
  1. Cellular Automata: A Discrete View of the World (Wiley Series in Discrete Mathematics & Optimization) by Joel L. Schiff, 2008-01-06
  2. New Constructions in Cellular Automata (Santa Fe Institute Studies in the Sciences of Complexity Proceedings)
  3. C++ Simulations and Cellular Automata by Scott Robert Ladd, 1995-10
  4. Cellular Automata: Theory and Experiment (Special Issues of Physica D)
  5. Cities and Complexity: Understanding Cities with Cellular Automata, Agent-Based Models, and Fractals by Michael Batty, 2007-09-30
  6. Quantum Cellular Automata: Theory, Experimentation And Prospects by Massimo Macucci (Editor), 2006-03-15
  7. Cellular Automata Modeling of Physical Systems (Collection Alea-Saclay: Monographs and Texts in Statistical Physics) by Chopard Bastien, Droz Michel, 2005-06-30
  8. Cellular Automata Machines: A New Environment for Modeling (Scientific Computation) by Tommaso Toffoli, Norman Margolus, 1987-04-22
  9. Game of Life Cellular Automata
  10. Nonlinear Workbook: Chaos, Fractals, Cellular Automata, Neural Networks, Genetic Algorithms, Gene Expression by Willi-Hans Steeb, 2008-06-17
  11. Cellular Automata: A Discrete Universe by Andrew Ilachinski, 2001-07-30
  12. Modeling Nature: Cellular Automata Simulations with Mathematica by Richard J. Gaylord, Kazume Nishidate, 1996-08-27
  13. Simulating Complex Systems by Cellular Automata (Understanding Complex Systems)
  14. Cellular Automata Transforms: Theory and Applications in Multimedia Compression, Encryption, and Modeling (Multimedia Systems and Applications) by Olu Lafe, 2000-01-15

1. Cellular Automaton - Wikipedia, The Free Encyclopedia
A cellular automaton (plural cellular automata) is a discrete model studied in computability theory, mathematics, theoretical biology and Microstucture
Cellular automaton
From Wikipedia, the free encyclopedia
Jump to: navigation search A cellular automaton (plural: cellular automata ) is a discrete model studied in computability theory mathematics theoretical biology and microstructure modelling. It consists of a 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 . 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 created.
edit Overview
One way to simulate a two-dimensional cellular automaton is with an infinite sheet of graph paper along with a set of rules for the cells to follow. Each square is called a "cell" and each cell has two possible states, black and white. The "neighbors" of a cell are the 8 squares touching it. For such a cell and its neighbors, there are 512 (= 2

2. Cellular Automata
Reversible cellular automata, neighbourhoods, billiard ball machines, Java applets. By Tim Tyler.
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Cellular automata Reversible cellular automata Introduction to reversible automata On reversible logic Designing reversible automata Billiard ball machines ... Cellular Automata Automata whose inverses have large neighbourhoods Automata whose inverses have unboundedly large neighbourhoods Invertable honeycomb automata ... automata Public key cryptography using cellular automata Public key cryptography using cellular automata Public key cryptography using cellular automata - bibliography Implementing automata in hardware Cellular automata hardware Hardware for cellular automata Crystalline computation Miscellaneous Composite automata Wolfram's numbering scheme for his "elementary" automata Isomorphic automata Neighbouring domains Cellular Automata FAQ Finite Nature Java applets Reaction-diffusion cellular automata ] - in [ Texture Garden Fractal Drainage ] - patterns caused by erosion and drainage Diffusion-limited aggregation ] - fractal growth Self-reproducing cellular automata HAL ] - self-reproducing universal cellular automaton HexHAL ] - hexagonal version of [ HAL Revoworms ] - reversible self-reproducing worms Crystal 1D ] - self-reproducing cellular automaton Crystal 2D ] - self-reproducing cellular automaton Physics Interference ] - interference patterns in a cellular automaton Fredkin CA ] - a 3D cellular automaton Solitons ] - omnidirectional gliders Reversible diffusion ] - reversible diffusion and lattice gasses Water simulation cellular automata ] - in [ Texture Garden Membrane models

3. Cellular Automata And The Edge Of Chaos
David J. Eck s Javaillustrated introduction to 1-dimensional cellular automata.
New in June 2004: A new version of EdgeOfChaos is available that can use file and save images (when run as an application). The new version requires Java 1.4 or higher. See Page 7 of this site for more information.
Cellular Automata
And the Edge of Chaos
A computer follows rules. At each moment, the rules determine exactly what the computer will do next. We say that a computer is an example of an automaton . Other, simpler examples of automata also exist. ( Automata is the plural of automaton .) These more abstract rule-following devices can be easier to study computers, and they can be interesting to study in their own right. One type of automaton that has received a lot of attention is cellular automata . For one thing, they make pretty pictures. For another, they are related to exciting new ideas such as artificial life and the edge of chaos. Here is a fairly simple example: An applet showing a cellular automaton
would appear here
in browsers that support Java. If you would like to learn more about cellualr automata, here are some pages of information and Java applets that you can look at. (The most interesting things here are the applet on page 6, and the newer version of the same applet on page 7, which can make some awfully nice pictures, such as this one (117 kilobytes).)

4. Cellular Automata
Each cell is a sort of very stupid computer in the jargon, a finite-state automaton - and so the whole board is called a cellular automaton, or CA.
Cellular Automata
28 Sep 2007 21:41 The chess-board is the world; the pieces are the phenomena of the universe; the rules of the game are what we call the laws of Nature.
-T. H. Huxley Take a board, and divide it up into squares, like a chess-board or checker-board. These are the cells. Each cell has one of a finite number of distinct colors - red and black, say, or (to be patriotic) red, white and blue. (We don't allow continuous shading, and every cell has just one color.) Now we come to the "automaton" part. Sitting somewhere to one side of the board is a clock, and every time the clock ticks the colors of the cells change. Each cell looks at the colors of the nearby cells, and its own color, and then applies a definite rule, the transition rule, specified in advance, to decide its color in the next clock-tick; and all the cells change at the same time. (The rule can say "Stay the same.") Each cell is a sort of very stupid computer - in the jargon, a finite-state automaton - and so the whole board is called a cellular automaton

5. Cellular Automata Laboratory
An extendable DOS/Windows application for exploring cellular automata, accompanied by a thorough user guide; by Rudy Rucker and John Walker.
by Rudy Rucker and John Walker
Introduction (from the User Guide
Cellular automata are self-generating computer graphics movies. The most important near-term application of cellular automata will be to commercial computer graphics; in five years you won't be able to watch television for an hour without seeing some kind of CA. Three other key applications of cellular automata will be to simulation of biological systems (artificial life), to simulation of physical phenomena (heat-flow and turbulence), and to the design of massively parallel computers. Most of the programs in the Rudy Rucker Cellular Automata Lab (CelLab) are two-dimensional cellular automata. In these programs the computer screen is divided up into "cells" which are colored rectangles or dots. Each cell is repeatedly "updated" by changing its old color to a new color. The net effect of the individual updates is that you see an ever-evolving sequence of screens. A graphics program of this nature is specifically called a cellular automaton when it is 1) parallel, 2) local, and 3) homogeneous. Parallelism means that the individual cell updates are performed independently of each other. That is, we think of all of the updates being done at once.

6. Cellular Automata FAQ
Definitions and general references on cellular automata; Packages for running cellular automata - and related systems;
Cellular Automata FAQ
Non-Java version Edited by Tim Tyler . Originally edited by Howard Gutowitz
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About this FAQ; What is the status of the Cellular Automata FAQ? Will there be a text version of the FAQ? Is the original FAQ still available? Why are Java applets stealing my CPU cycles? ... Generalities Definitions - and general references on cellular automata; What are Cellular Automata (CA)? How do I contribute bibliographic material to the FAQ? Where are cellular automata discussed? What should I work on in CA for my Ph.D. thesis? ... Cellular automata software Packages for running cellular automata - and related systems; What general-purpose CA simulators are available? What simulators for the Game of Life are available? How can I make CA simulations run fast? What other CA software is available? ... Cellular automata hardware Running cellular automata in hardware; What hardware implementations exist for CA? Are there any simulators for CAM? What about running CA's on parallel or distributed machines? References ... Conway's game of life All about Conway's Game of Life [life-specific software here]; Where do I start?

7. Mathematics Archives - Topics In Mathematics - Cellular Automata
KEYWORDS Complex Systems, Random Interaction, Artificial Life, Software; Tutorial on cellular automata ADD. KEYWORDS Game of Life, Forest Model
Topics in Mathematics Cellular Automata

8. Modern Cellular Automata - Live Color Cellular Automata
Java powered plethora of live color cellular automata with traditional, fractal, pattern, and unique hexagonal cellular automata. Fast free software.
Java powered plethora of live color cellular automata with traditional, fractal, pattern, and unique hexagonal cellular automata. Fast free software. The redistributable Modern Cellular Automata applet provides a powerful fast cellular automata engine suitable both for presentation and experimentation. Both Java and Javascript must be enabled in your browser for proper use of this site. document.writeln('Modern Cellular AutomataModern CA Entrance') Traditional Rules August Addition Out Of It Rule Mix Lab Some Other Rules ... Author Internet Explorer is three times faster on this site with Java 2, free from Sun Microsystems Visit the Color Game Of Life Visual Exhibition sister site Map

9. Grant Robinson : Cellular Automata Launcher
cellular automata. cellular automata. Click to launch project Click to launch project. About cellular automata. I was inspired to make these small apps Projects
Cellular Automata
About Cellular Automata
I was inspired to make these small apps after reading Emergence: The Connected Lives of Ants, Brains, Cities, and Software by Steven Johnson (a great read btw, highly recommended). I'm fascinated by how a seemingly complex organic system can be created from such a simple set of rules. Make sure you try creating your own initial setup to see how it survives. If you like this you're likely to love Life vs Life a fun multiplayer game made by Volcano Kit based on the same principles. This app requires version 7 of the Flash player or higher to run, you can get the latest version here donate today

10. Stephen Wolfram: Articles On Cellular Automata
Technical articles by one of the leading CA researchers, concerning both 1D and 2D cellular automata.

Publications by Stephen Wolfram
Stephen Wolfram: Articles on Cellular Automata
Cellular Automata as Simple Self-Organizing
Statistical Mechanics of Cellular Automata Cellular Automata ... Cellular Automaton Supercomputing
Note: Since 1987 Stephen Wolfram's intellectual efforts
have primarily been described in his books on Mathematica
and A New Kind of Science rather than academic articles.

11. Introduction To Cellular Automata
Introduction to cellular automata illustrated by two programs. The text is available in PDF.

Introduction to Cellular Automata
Cellular Automata Viewer
is a cellular automata manager. Version 2.0 Small but complete, it will allow you to explore Conway's universe (the famous Game of Life) as well as more complex and sophisticated universes (Brian's Brain, Swirl...). Version 2.0 implements some 1D cellular automata. Logicell
is an applet which demonstrates the capability of a Conway Cellular Automaton to manage boolean operators. It is illustrated with some automatism applications (binary adder, two-way switch...).
ome Cellular Automata Biomorphs ... Links
Last Update 6 May, 2006 audit et mesure d'audience visiteurs internet par

12. Cellular Automata
A Java applet demonstrating cellular automata models of cardiac dynamics; by Gil Bub.
Optical Mapping introduction exp. methods data analysis image database ... movie samples
Excitable Media introduction examples
Links In the Press Research MITACS Science ... General
Contact mcgill lab email me my homepage optical mapping pages site map about
Cellular Automata Examples
The applet on this page is a simple Greenburg Hastings type cellular automaton (CA). In a CA, each cell has a finite number of states, which are updated based on its neighbours and its own state the previous time step. In CA models of cardiac dynamics, the cells are either active, refractory or excitable. The length of time each cell spends in each state, as well as the size of the neighbourhood and the threshold for activation, are all adjustable parameters. A similar model is formally described here
Any questions or comments? Contact Spiral waves.
Spirals have different characteristics for different parameters. Control-click in the window to bring up a graph that shows the period of the spiral.
Neighbourhood=1, E=8, R=10, threshold=3

13. Cellular Automata
Part II Inverting Local Structure Theory Equations to Find cellular automata With Specified Properties}, booktitle = {Learning and RecognitionA Modern

14. Mirek's Java Cellebration
Mirek s Java Cellebration (MJCell) is a Java applet that allows playing 300+ cellular automata rules and 1400+ patterns. It can play rules from 13 CA rules
Mirek's Java Cellebration v.1.50 what's new?
Go back to MCell Home Mirek's Java Cellebration (MJCell) is a Java applet that allows playing 300+ Cellular Automata rules and 1400+ patterns. It can play rules from 13 CA rules families: Generations Life Vote Weighted Life ... Larger than Life , and some of the User DLLs . It allows also to experiment with own rules. The applet is a simplified version of MCell. It does not offer extended features of MCell, but has one advantage over it: its usage is not restricted to MS Windows. Full source code of the applet is available here . You can also download the full off-line version equipped in a rich library of patterns. You should also download this version if you plan to put the MJCell applet on your own Web page. To start the applet, click on the "Start" button below. The applet will show up in its own window. For the description of all rules available in the applet refer to the CA rules page Sign my MJCell GuestBook Read my MJCell GuestBook
[ GuestBook by

15. Cellular Automata Miscellanea
A repository with cellular automata related papers, lectures and software concentrating on Rule 110 by Harold V. McIntosh.
Cellular Automata Miscellanea
Instituto de Ciencias
Universidad La Salle

Last modified: May 15, 2007.
To send mail to Harold V. McIntosh , please click here: here to send mail to
This page is best viewed with: cellular automata, CELLULAR AUTOMATA cellular automaton, CELLULAR AUTOMATON mean field theory, MEAN FIELD THEORY universal computation, UNIVERSAL COMPUTATION complex systems, COMPLEX SYSTEMS camex, CAMEX nxlcau, NXLCAU life, LIFE lcau, LCAU de Bruijn Diagrams, de bruijn diagrams reversible cellular automata collective behaviour, collective behavior collective behaviour in cellular automata, collective behavior in cellular automata

16. 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.
Cellular Automaton
Content on this website
Links to other websites
27. April 2005

17. Homepage Alexander Schatten - Information / Tutorials
A cellular automata tutorial that covers the structure, behaviour and some applications of CA and offers a philosophical background as well; by Alexander
Homepage Alexander Schatten - Information / Tutorials Home


Main Interests


... And now to something completly different...
Cellular Automata Tutorial
1. Introduction
From the theoretical point of view, Cellular Automata (CA) were introduced in the late 1940's by John von Neumann (von Neumann, 1966; Toffoli, 1987) and Stanislaw Ulam. From the more practical point of view it was moreless in the late 1960's when John Horton Conway developed the Game of Life (Gardner, 1970; Dewdney, 1989; Dewdney, 1990). CA's are discrete dynamical systems and are often described as a counterpart to partial differential equations , which have the capability to describe continuous dynamical systems. The meaning of discrete is, that space, time and properties of the automaton can have only a finite, countable number of states. The basic idea is not to try to describe a complex system from "above" - to describe it using difficult equations, but simulating this system by interaction of cells following easy rules. In other words: Not to describe a complex system with complex equations, but let the complexity emerge by interaction of

18. Cellab Downloads From Rudy Rucker's Website
Rudy Rucker s Cellab cellular automata Page. Download John Walker and Rudy Rucker s cellular automata Laboratory Software as an archive file, CELLAB2.
Cella b Downloads Home Biography Books Writing ... Email Seek Ye the Gnarl! This is a public domain freeware program by John Walker and Rudy Rucker. The Cellab Cellular Automata Laboratory is the Windows version of a package originally called CA Lab: the Rudy Rucker Cellular Automata Laboratory , and sold by Autodesk, Inc. The main Cellab program JC.EXE was written by John Walker and includes some rules by Rudy Rucker. Enjoy it, back at last, the fastest and best 2D cellular automata program ever written! Download John Walker and Rudy Rucker's Cellular Automata Laboratory Software as an archive file, CELLAB2.ZIP If you live in Europe and have trouble with the download, go to John Walker 's site, which is in Switzerland. CELLAB2.ZIP includes the JC.EXE program by John Walker, which is a Windows port of a the CA.EXE program which was formerly sold by Autodesk as CA LAB. In addition there are a number of new JC rules which were not in the CA LAB release. The CA LAB DOS-window program RC.EXE by Rudy Rucker is included as well. The CelLab software and its support files are being distributed as public domain freeware and may be used for any purpose without obtaining permission from Walker and/or Rucker.

19. Journal Of Cellular Automata
RECOMMEND THE JOURNAL OF cellular automata TO YOUR LIBRARY CALL FOR PAPERS (download PDF file). OCP Science Journals

20. Quantum-dot Cellular Automata Homeworld
QCA is QuantumDot cellular automata, leading research in more powerful computing with faster microelectronics.
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