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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. TUTORIAL NOTES - Cellular Automata
preprint may be copied and used provided that this notice and the authorship details remain attached. cellular automata
This preprint may be copied and used provided that this notice and the authorship details remain attached.
David G. Green
Environmental and Information Sciences
Charles Sturt University
The increasing prominence of computers has led to a new way of looking at the world. This view sees nature as a form of computation. That is, we treat objects as simple computers, each obeying its own set of laws. The "cellular automaton" extends this analogy to provide a way of viewing whole populations of interacting "cells", each of which is itself a computer (automaton). By building appropriate rules into a cellular automaton, we can simulate many kinds of complex behaviour, ranging from the motion of fluids governed by the Navier-Stokes equations to outbreaks of starfish on a coral reef.
A cellular automaton is an array of identically programmed automata, or "cells", which interact with one another. The arrays usually form either a 1-dimensional string of cells, a 2-D grid, or a 3-D solid. Most often the cells are arranged as a simple rectangular grid, but other arrangements, such as a honeycomb, are sometimes used. The essential features of a cellular automaton ("CA" for short) are:
  • its STATE is a variable that takes a different separate for each cell. The state can be either a number or a property. For instance if each cell represents part of a landscape, then the state might represent (say) the number of animals at each location or the type of forest cover growing there.

2. EvCA Main Page
Welcome to the Evolving cellular automata (EvCA) group home page!The EvCA group is based at the Santa Fe Insitute (SFI) and at
Welcome to the Evolving Cellular Automata (EvCA) group home page!
The EvCA group is based at the Santa Fe Insitute (SFI) and at the Los Alamos National Laboratory (LANL) at the Biophysics Group
Santa Fe Institute
1399 Hyde Park Road
Santa Fe, NM 87501 Phone: (505) 984-8800
Fax: (505) 982-0565
Los Alamos National Laboratory
Biophysics, P-21
Mail Stop D454
Los Alamos, NM 87545 Phone: (505) 665-2545
The overall research done by the EvCA group is primarily motivated by the question: " How does evolution produce sophisticated emergent computation in systems composed of simple components limited to local interactions? " To try to find answers to this question, genetic algorithms are used to evolve cellular automata to perform computational tasks that require global information processing. In studying the results of these computer simulations, many more, related questions have sprung up, ranging from questions about the relation between pattern formation and information processing to questions about population dynamics and coevolution. Follow the links in the list below to find out more about these research projects, and how they relate to each other.
The EvCA group is headed by physicist James P. Crutchfield (SFI) and computer scientist Melanie Mitchell (LANL/SFI). At any time, the group is complemented by a number of graduate students and postdoctoral fellows. Below is a list of the current and former group members. Clicking on a name will take you to the personal home page of the respective group member. Or you can send any of us email by clicking on the respective group member's email address.

3. Cellular Automata And The Edge Of Chaos
Author David J. Eck offers a Javabased example of one-dimensional CA. Check out reports and source coding.
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 thing here is the applet on page 6, which can make some awfully nice pictures.)
  • About Cellular Automata
  • Instructions for using the HandCraftCA Applet
  • The HandCraftCA Applet
  • The Edge of Chaos ...
  • Bibliography The source code for the applets used on these pages is available here:
  • 4. Cellular Automata
    cellular automata are discrete dynamical systems whose behaviour is completely specified in terms of a local relation. A cellular automaton can be thought of as a stylised universe.
    Cellular Automata Cellular automata are discrete dynamical systems whose behaviour is completely specified in terms of a local relation. A cellular automaton can be thought of as a stylised universe. Space is represented by a uniform grid, with each cell containing a few bits of data; time advances in discrete steps and the laws of the "universe" are expressed in, say, a small look-up table, through which at each step each cell computes its new state from that of its close neighbours. Thus, the system's laws are local and uniform. Conway's Game of Life Wolfram's Cellular Automata One-dimensional cellular automata Inhomogeneous cellular automata ... Packard's Snowflakes Mathematician Stanislaw M. Ulam liked to invent pattern games for the computer at Los Alamos. Given certain fixed rules, the computer would print out ever-changing patterns. Many patterns grew almost as if they were alive. A simple square would evolve into a delicate, coral-like growth. Two patterns would "fight" over territory, sometimes leading to mutual annihilation. He developed 3-D games too, constructing thickets of coloured cubes as prescribed by computer. He called the patterns "recursively defined geometric objects". Ulam's games were cellular games. Each pattern was composed of square (or triangular or hexagonal) cells. In effect, the games were played on limitless chessboards. All growth and change of patterns took place in discrete jumps. From moment to moment, the fate of a given cell depended only on the states of its neighbouring cells.

    5. Missing Page
    home information/tutorial cellular automata. main navigation
    Missing Page
    Santa Fe Institute Quick Search
    SFI Home Page

    Business Network


    Find Us

    Santa Fe Institute
    Last update:
    Wednesday, May 9, 2001
    at 10:10:50 AM MST by Webmaster OOPS! Alife has moved to Please note that any web pages associated with no longer exist on this server. Please don't send us e-mail about alife pages. Instead point your browser to the URL above.

    6. EvCA Papers
    Evolving cellular automata with Genetic Algorithms. Coevolution. Resource Sharingand Coevolution in Evolving cellular automata. Ph.D. Dissertations.
    EvCA Papers
    This page contains a list of all papers relating to the EvCA project. The papers are grouped according to main research topic. There is also a category for Ph.D. dissertations written by (former) graduate students in the EvCA group. Click on a reseach topic in the list below or scroll down the page to find the paper(s) of your interest. Click on the title of a paper to see the complete reference information, the abstract, and a link to a postscript version of the respective paper. Please contact us if you have trouble downloading any of these papers. In some cases we might be able to send a hardcopy.
    Evolving Cellular Automata with Genetic Algorithms
    Computational Mechanics
    • Pattern Discovery and Computational Mechanics
    Population Dynamics

    7. Stephen Wolfram: Articles On Cellular Automata
    Examine "cellular automata " "Approaches to Complexity Engineering " and other articles written by Stephen Wolfram

    Cellular Automata
    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.

    8. Complex Systems Virtual Library By Themes - Cellular Automata
    Complex Systems VL by themes - cellular automata. Info cellular automata Afew animations of cellular automata (CA) made by Juha Haataja at CSC.
    Complex Systems VL- by themes - Cellular Automata
    HTML Created: 17 Aug 2001 15:00:25
    Artificial Life Packages
    This directory contains artificial life software packages.
    Bibliography of Complexity Measures
    This is a bibliography covering some of the philosophical and practical references to the concept and measurement of Complexity. It does not a ttempt to cover all the new sciences that might come under the "Complexity" banner, unl ess they are relevant to the idea of Complexity per se. Also, it does not include a very comprehensive amount on Computational Complexity due to restr ictions on time and space.
    Cellular Automata
    A few animations of cellular automata (CA) made by Juha Haataja at CSC.
    Cellular Automata and Complexity: Collected Papers
    A collection of Stephen Wolfram's original papers on cellular automata and complexity.
    Cellular Neural Networks (CNN)
    Cellular Neural Networks (CNN) is a massive parallel computing paradigm defined in discrete N-dimensional spaces.
    Chaos and Complex Systems Seminar
    The Chaos and Complex Systems Seminar is a weekly, campus-wide, interdisciplinary seminar series at the University of Wisconsin - Madison on the new sciences of chaos and complexity. Talks span a wide range of topics including computer science, mathematics, economics, biology, meteorology, psychology, and physics. They are aimed at a non-expert but scientific audience, and everyone is welcome.
    Chief Science Officer
    Corneal Aberration removal, cortithalmas imaging, visuocortical projection, GABA production and stimulation, absorption visualisation

    9. Cellular Automata
    Introduction to 1D and 2D CA by Andreas Ehrencrona. Java applets.Category Computers Artificial Life cellular automata...... cellular automata could reveal a lot about how the universe works and maybe evenabout how life began. cellular automata. Onedimensional cellular automata.

    10. Cellular Automata - Digital Worlds Tutorial
    An essay by Alexander Schatten.Category Computers Artificial Life cellular automata...... Back to Contents. Building cellular automata. The Cell. The basic element of aCA is the cell. Back to Contents. cellular automata vs. Differential Equations.
    Portal Page: Alexander Schatten home information/tutorial main navigation Home Main Interest / Projects Information / Tutorials Publications ...
    printer friendly version (no navigation bar)
    Cellular Automata
    Digital Worlds
    written by Alexander Schatten
    This is the first version, last update on Oct.5 th
    • Introduction and History
    • A Glance at Dynamical Systems and Chaos
    • Building Cellular Automata Back to Information / Tutorial Page
      Introduction and History
      From the theoretical point of view, Cellular Automata Game of Life (Gardner, 1970; Dewdney, 1989; Dewdney, 1990). 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

    11. Cellular Automata
    cellular automata. (Tue May 14 175859 2002)
    Cellular Automata
    (Tue May 14 17:58:59 2002) 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

    12. Java CA Applet
    Christopher Osborn's Java applet exploring self-reproducing patterns.Category Computers Artificial Life cellular automata......This page has been moved to my new site at Pleaseemail me if you cannot find the page you are looking for.
    This page has been moved to my new site at Please e-mail me if you cannot find the page you are looking for. (Chris Osborn 18 th January 2002

    13. About Cellular Automata
    Introdution to. Onedimensional cellular automata. A one-dimensional cellularautomaton consists of two things a row of cells and a set of rules .
    Introdution to
    One-dimensional Cellular Automata
    A one-dimensional cellular automaton consists of two things: a row of "cells" and a set of "rules". (There are also two-dimensional cellular automata, which use rectangular grids of cells, but from now on when I say "cellular automaton" or just "CA", I will mean "one-dimensional cellular automaton".) Each of the cells can be in one of several "states". The number of possible states depends on the automaton. Think of the states as colors. In a two-state automaton, each of the cells can be either black or white. Of course, you might just as easily use purple and orange to represent the states, if you thing that's prettier. In a three-state automaton, the states might be black, red, and blue. A CA doesn't just sit there. Over time, the cells can change from state to state. The cellular automaton's rules determine how the states change. It works like this: When the time comes for the cells to change state, each cell looks around and gathers information on its neighbors' states. (Exactly which cells are considered"neighbors" is also something that depends on the paticular CA.) Based on its own state, its neighbors' states, and the rules of the CA, the cell decides what its new state should be. All the cells change state at the same time. You should think of the row of cells as a miniature "world" that runs through a sequence of "years" or "generations." At the end of each year, all the cells simultaneously decide on their state for the next year.

    14. CSC
    cellular automata. CSC Mathematical Topics Here are a few animations of cellularautomata (CA) made by Juha Haataja at CSC. 1D cellular automata.
    Contacts Feedback
    Search ... Scientist's interface Services Customer information Funet and networking Publications Supported sciences Computers Information services
    Cellular Automata
    Visualizations Home page Help End of the page ... Comments Cellular automata are simple discrete dynamical systems. Here are a few animations of cellular automata (CA) made by Juha Haataja at CSC.
    1D Cellular Automata
    2D Cellular Automata
    • Animation of a 2D cellular automaton exhibiting self-organization (970 kB of data).
    • Animation of a simple 2D cellular automata generating a fractal structure (840 kB of data).
    • Animation of a 2D "sandpile" automaton (790 kB of data).
    3D Cellular Automata
    • Animation of a 3D "forest fire" cellular automaton (370 kB of data).
    Visualizations Home page Back Help ... Comments Last modified: February 25, 2002 05:42:38

    15. Cellular Automata Laboratory
    CelLab manuals on-line by Rudy Rucker and John Walker.Category Computers Artificial Life cellular Rudy Rucker and John Walker. Introduction (from the User Guide ).cellular automata are selfgenerating computer graphics movies.
    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.

    16. Cellular Automata Laboratory
    Exploring cellular automata. by Rudy Rucker and John Walker. cellular automata TheoryNeighbors; Vote and Other Totalistic Rules; Life; Brain; Semitotalistic Rules;
    Exploring Cellular Automata
    by Rudy Rucker and John Walker
    Table of Contents

    17. Capow
    Rudy Rucker's ongoing research project. Features new kinds of continuousvalued cellular automata Category Computers Artificial Life cellular automata......This page has been moved to. http//
    This page has been moved to

    18. Cellab Downloads From Rudy Rucker's Website
    The Cellab cellular automata Laboratory is the Windows version of a package originallycalled CA Lab the Rudy Rucker cellular automata Laboratory, and sold by
    Cella b Downloads Home Page Biography Works Online ... 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. Cellular Automata
    Reversible cellular automata, neighbourhoods, billiard ball machines, Java applets. By Tim Tyler.Category Computers Artificial Life cellular automata......cellular automata. Introduction Isometric cellular systems; Bijective cellularsystems; Neighbourhood survey; cellular automata optimisation; Definition
    Cellular automata
  • Public key cryptography using cellular automata (with bibliography Composite automata Implementing automata in hardware Hardware for cellular automata ... Isomorphic automata
  • Neighbouring domains
    Java applets
    Tim Tyler

    20. Cellular Automata Links
    Builder in Japan Stephen Wolfram's CA papers Bruce M. Boghosian CA simulatingphysical phenomena CA mailing list 1D cellular automata - illustrating some
    Java CA simulators
    Other CA simulators
    Mirek's comprehensive list of simulators
    Mirek's Cellebration
    - by Mirek Wojtowicz
    - George Maydwell's Windows-based "Animation reduction" automata
    - Windows CA explorer - by Ben Schaeffer
    - Windows - by Rudy Rucker and John Walker
    - CAs for the X window system


    An old list of simulators
    Langton-like loops

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