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         Cellular Automata:     more books (100)
  1. Cellular Automata with Memory by Ramon Alonso-Sanz, 2009-06-01
  2. Cellular Automata and Groups (Springer Monographs in Mathematics) by Tullio Ceccherini-Silberstein, Michel Coornaert, 2010-09-02
  3. Modern Cellular Automata: Theory and Applications (Advanced Applications in Pattern Recognition) by Kendall Preston Jr., Michael J.B. Duff, 1985-02-28
  4. Cellular Automata And Complexity: Collected Papers by Stephen Wolfram, 1994-02-21
  5. Essays on Cellular Automata
  6. Models of Massive Parallelism: Analysis of Cellular Automata and Neural Networks (Texts in Theoretical Computer Science. An EATCS Series) by Max Garzon, 1995-07-18
  7. Design and Test of Digital Circuits by Quantum-Dot Cellular Automata by Fabrizo Lombardi, Jing Huang, 2007-10-31
  8. Nonlinear Physics for Beginners: Fractals, Chaos, Solitons, Pattern Formation, Cellular Automata and Complex Systems by Lui Lam, 1998-07
  9. Cellular Automaton Modeling of Biological Pattern Formation by Andreas Deutsch, Sabine Dormann, 2004-10-28
  10. Cellular Automata and Complex Systems: Methods for Modeling Biological Phenomena (Premier Reference Source) by Eleonora Bilotta, 2010-06-30
  11. Automata-2008: Theory and Applications of Cellular Automata
  12. Additive Cellular Automata: Theory and Applications (Practitioners) by Parimal Pal Chaudhuri, Dipanwita Roy Chowdhury, et all 1997-07-11
  13. Cellular Automata: A Parallel Model (Mathematics and Its Applications)
  14. Computational Analysis of One-Dimensional Cellular Automata (World Scientific Series on Nonlinear Science. Series a, Vol 15) by Burton H. Voorhees, 1996-02

21. Gliders In "Life"-Like Cellular Automata
An online interactive database of rules with gliders, by D. Eppstein.
Which "Life"-Like Systems Have Gliders?
John Conway's "Game of Life" has fascinated and inspired many enthusiasts, due to the emergence of complex behavior from a very simple system. One of the many interesting phenomena in life is the existence of "gliders": small patterns that move across the grid. Some authors have asserted that the gliders and other complex behaviors occurring in Life are unusual, for instance Wolfram: "Except for a few simple variants on the Game of Life, no other definite class-4 two-dimensional cellular automata were found in a random sample of several thousand outer totalistic rules." Are gliders really so rare? I have investigated whether gliders exist in many semitotalistic rules similar to Life, where the behavior of a cell depends only on its own state and the number of live neighbors. The results show that the existence of gliders is commonplace, contradicting Wolfram and calling into question his classification of cellular automata Jason Summers' c/5 diagonal spaceship in Life Online interactive database of rules with gliders Paper describing my glider search program and MSRI talk on streaming video Rules with self-replicating patterns
New! Replicators in rules with B0, July 2002

22. Cellular Automata And Music
Take computers, mathematics, and the Java Sound API, add in some Java code, and you ve got a recipe for creating some uniquely fascinating music.
Country/region select Home Products My account ... developerWorks
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The IBM developerWorks Web site is currently under maintenance.
Please try again later. Thank you.
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23. Java CA Applet
Self Reproducing cellular automata Loops has moved to
Self Reproducing Cellular Automata Loops has moved to

24. Isle Ex: Transmusic: Cellular Automaton Music
Music samples generated using some popular cellular automata rules; by John Elliott.
cellular automaton music ~ The examples here assembled, though crude, will I hope suffice to convey a sense of the potential for generating music using cellular automata, as well as for better understanding the structure of CA evolution by making use of the aural modality. Parity music
Fredkin's unique Parity rule abounds in spontaneous musicality. CyclicCA music
"Transcendigital" meditation at period 14 in three easy lessons, courtesy of the CyclicCA Brain music
We knew the bizarre gliderworld of Brian's Brain rule could dance. Turns out it can sing too. More CA music
A few token musifications of other CAs, including Conway's Life and Banks' Computer Background information
What's a CA orbit? How can it be musified? If you've got questions, we've got answers. The Cellsprings Java applet
Explore the CAs behind the music, and many others. ~ isle ex ~ HOME SITE MAP WHAT'S NEW CONTACT Page created 4-Feb-1998. See map for file modification date.

25. Cellular Automata
An interactive cellular automata generator with C++ source code available for downloading; by Kevin McDermott.
Main Generate Cellular Automata Play and Download Sudoku The Cellular Automaton The source code to my Cellular Automaton image generator can be found here . It is C++ source code that outputs a raw pgm image file to stdout. It should compile under most C++ compilers, although it has only been tested with the g++ compiler on Linux. I am releasing it under the GNU Public License (GPL), so do with it as is appropriate under that license. The cellular automaton consists of a line of cells, each colored either black or white. At every step there is then a definite rule that determines the color of a given cell from the color of that cell and its immediate left and right neighbors on the step before. -Stephen Wolfram (A New Kind of Science, 2004) Cellular automata are extreamly simple computational systems that create interesting images which show some even more interesting behaviours. Essentially, these images show the product of thousands of simple computations based on rules that should be followed regarding a pixel's imediate neighbours. These cellular automata images are a bunch of black and white pixels that are built from the top down, where each scanline is based on the colour of the pixels on the scanline above it. More specifically, the pixels imediately above it, above it and to the left, and above it and to the right. So each pixel's colour is determined by three other pixels.

26. Evolving Cellular Automata Group - The Santa Fe Institute
Development and research of evolving cellular automata with genetic algorithms, computational mechanics, population dynamics and coevolution.
J. Crutchfield Computational Mechanics Dynamics of Learning Evolving Cellular Automata ... Funding
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

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.
Santa Fe Institute
1399 Hyde Park Road
Santa Fe, NM 87501

27. Five Cellular Automata
Windows software for exploring five cellular automata qstate Life (a generalization of Conway s Life), the Belousv-Zhabotinsky Reaction, Togetherness,
Five Cellular Automata Introduction The five cellular automata:
  • q-state Life
  • The Belousov-Zhabotinsky Reaction
  • Togetherness
  • Viral Replication ...
  • Updates Here are successive images (reduced by 50% in width and height) showing typical screens for all five cellular automata (these are snapshots of dynamic screens): Fullsize screenshots are given in the subsections of this documentation. Introduction A cellular automaton consists of:
    (b) A set of values or "states" such that each cell is associated with a particular state.
    A simple and well-known example of a cellular automaton is John Conway's Life. In this we consider a square array of cells, each of which is either "dead" or "alive". The eight cells immediately adjacent to a cell are called its "neighbors". The rules governing the dynamics of the system are as follows: (i) In the transition from one "generation" to the next the state of each cell is changed once according to rules (ii) and (iii).
    (ii) A cell which is alive will remain alive in the next generation if there are two or three cells among its eight neighbors which are alive; otherwise it dies.
  • 28. Topic: Areas/ca/
    Tommaso Toffoli and Norman Margolus, cellular automata Machines A New Environment Keywords AI Software Packages, cellular automata, Software Packages
    CMU Artificial Intelligence Repository
    Cellular Automata
    areas/ca/ faq/ Cellular Automata FAQ: Frequently Asked Questions About Cellular Automata mail/ Mail archives for the CA mailing list systems/ Cellular Automata Packages See Also: areas/genetic/ areas/alife/ Origin: FTP repositories for cellular automata include* This directory contains software and materials concerning cellular automata and related topics. References: Forrest, S., editor, "Emergent Computation", MIT Press, 1991. J. D. Farmer, T. Toffoli, and S. Wolfram, "Cellular Automata", North-Holland, Amsterdam, 1984. Howard Gutowitz, "Cellular Automata: Theory and Experiment", MIT Press, Cambridge, MA 1991. ISBN 0-262-57086-6. Tommaso Toffoli and Norman Margolus, "Cellular Automata Machines: A New Environment for Modeling", MIT Press, 1987. Andrew Wuensche and Mike Lesser, "The Global Dynamics of Cellular Automata", Addison-Wesley, 1992. IBSN 0-201-55740-1. CD-ROM: Prime Time Freeware for AI, Issue 1-1 Mailing List: comp.theory.cell.automata, comp.theory.self-org-sys The mailing list (aka is gatewayed to comp.theory.cell.automata. To join, send mail to Keywords: AI Software Packages, Cellular Automata, Software Packages Last Web update on Mon Feb 13 10:20:18 1995

    29. Mirek's Cellebration - 1-D And 2-D Cellular Automata Viewer, Explorer And Editor
    Mirek s Cellebration, 1D and 2-D cellular automata viewer, explorer and editor.
    Welcome to Mirek's Cellebration
    1D and 2D Cellular Automata explorer
    by Mirek Wojtowicz
    Cellular Automata
    What is MCell?

    CA rules lexicon

    CA gallery
    ... Home T his site is devoted to Cellular Automata, one of the most intriguing and admirable aspects of mathematics. Perhaps you have already heard about the Game of Life, one of oldest and best-explored Cellular Automata. Game of Life is only a tip of a large cellular iceberg. Actually, the count of even simple Cellular Automata is estimated to be *much* larger then the count of particles in our Universe! I decided to explore a bit of this huge world. To do it I developed my own Cellular Automata simulator, MCell, and with help from many people I collected a big library of Cellular Automata families, rules, and patterns. You can see much of my collection on these pages. Anyhow, the pages show only a static side of Cellular Automata. Cellular Automata are in fact very dynamic, so I strongly encourage you to download the free MCell software and/or run the MJCell Java applet to see the patterns running! And then, who knows, maybe you will also add something new to the Cellular Automata world?

    30. Game Studies 0102: Sims, BattleBots, Cellular Automata, God And Go. By Celia Pea
    Most simulation processes, such as system dynamics or cellular automata, destroy information. CP So you have to figure out what the systemic memory looks
    the international journal of computer game research
    volume 2, issue 1

    July 2002
    home about ... archive Celia Pearce is a game designer, artist, teacher and writer. She is the designer of the award-winning virtual reality attraction Virtual Adventures: The Loch Ness Expedition , and the author of The Interactive Book: A Guide to the Interactive Revolution (Macmillan, 1997) as well as numerous essays on game design and interactivity. She currently holds a position as Lecturer in Studio Art at the University of California Irvine's Claire Trevor School of the Arts.
    Sims, BattleBots, Cellular Automata God and Go
    A Conversation with Will Wright by Celia Pearce
    Conducted in Will Wright's office at Maxis, September 5, 2001 CP: What is your philosophy of interactive design? WW: Ooh, a heavy question, a philosophy question. they CP: When you were first working on SimCity , what was going on in the game world at that time? Were you responding to games that were out there, were you wanting something different? Were there things that influenced you at all in the game world or were you just totally in a different mindset? Pinball Construction Set by Bill Budge which was great. He was kind of playing around with the first pre-Mac Lisa interface, which was icon-based. He actually put this in the game, even though it was an Apple 2 game. He kind of emulated what would later become the Mac interface. But it was very easy to use, and you would create pinball sets with it which you could then play with. I thought that was very cool.

    31. SRCA
    cellular automata application with rules exploring self reproducing patterns.
    SRCA History Introduction Download ... Applet
    SRCA is a Cellular Automata (CA) Java application that implements some complex CA rules that give rise to self reproducing and evolving patterns. This application improves upon my original 'Self Reproducing Cellular Automata Loops' applet, with a better user interface, more functionality and more rules. The original applet is still available here if for some reason you cannot run SRCA. Please note that at present it is not possible to write your own CA rules for SRCA, but you can load/edit/save patterns and change some of optional parameter values on the existing rules. Moreover, SRCA is highly specialized in order to run certain types of rule well. See introduction for more details. I welcome any comments you may have on SRCA and related issues - see bottom of page for contact details. The image below is a screen shot of SRCA taken after running the SRL(8) rule on the default starting pattern for the indicated number of clock ticks. The two single loops that comprise the initial starting pattern have replicated and evolved into several colonies of different loop types, each competing for space. Basically this is a simulation of a very simple artificial universe in which self-replicating patterns grow, produce children, and eventually die. These self-reproducing patterns can be thought of as artificial primitive life forms. Initially the universe contains one or more loops (depending upon universe size). Each loop is a wire around which signals propagate. These signals are instructions for growing a child wire loop. Once a child loop has been grown, the signals from the parent loop are copied into it and it is then detached from the parent. The child then becomes a parent by growing its own children. As signals propagate along the wires there is a small possibility of corruption, causing mutant children and thus enabling gradual evolution of the wire loops into different shapes and sizes (and sometimes other transient structures). Wires have a finite lifetime, after which they decay into nothing.

    32. Cellular Automaton
    cellular automata are the simplest models of spatially distributed processes. They consist of an array of cells, each of which is allowed to be in one of a
    Cellular Automata (1947-present)
    Cellular automata are the simplest models of spatially distributed processes. They consist of an array of cells, each of which is allowed to be in one of a few states. At the same time, each cell looks to its neighbors to see what states they are in. Using this information each cell applies a simple rule to determine what state it should change to. This basic step is repeated over the whole array, again and again. Some of the patterns produced, by several simple cellular automata, are shown on this page.
    Cellular automata were invented in the 1940's by the mathematicians John von Neuman and Stanislaw Ulam, while they were working at the Los Alamos National Laboratory in northern central New Mexico. The most famous cellular automaton is the "Game Of Life" invented by mathematician John Conway, in the 1960's. Despite the simplicity of the rules governing the changes of state as the automaton moves from one generation to the next, the evolution of such a system is complex indeed.
    For interactive cellular automata simuations, go to Prof. David Griffeath's Java-based page

    33. GalaxyGoo Blogs: Cellular Automata - Custom Random Rulesets
    I ve done work with cellular automata in the past, including some different versions of Langtons Ants. Langtons Ant is a simple 2dimensional automata with
    GalaxyGoo Blogs
    Science, Art, Education, Technology, Science and Data Visualization...
    Cellular Automata - Custom Random Rulesets
    I've done work with Cellular Automata in the past, including some different versions of Langtons Ants. Langtons Ant is a simple 2-dimensional automata with a very simple ruleset, and it could produce some very interesting behaviors. However it was very limited on it's own, even with it's long life cycle. ~Mike Author: Mike Johnson
    Author's comments:
    Here we have a 2-dimensional automata ( an ant or termite is a common term ) that has a custom ruleset that is generated randomly. This ruleset could just be 2 rules long ( like Langtons Ant is ) or it could be up to 7 rules long. These rulesets can produce some very interesting emergent behavior. Some of them may produce purely chaos for their entire lifecycle, some may start out producing patterns that are bilaterally symmetrical, some may fluctuate between behaviors, and more - the possibilities are almost endless. To keep things interesting, there is a limitation of how many generations the automata will be allowed to run before the grid and automata are reset with a new random ruleset. In addition, you can force a reset of the system by hitting "r" on the keyboard at any time.

    34. Conway's Game Of Life
    SARCASim by George Maydwell, also for Windows, is a more generalpurpose cellular automata program. The acronym stands for Super Animation-Reduction
    [no java] Home Patterns too big for the applet About the Applet
    Conway's Game of Life
    A pop-up Java applet (see button, left) that displays a collection of the greatest patterns ever created in Conway's Game of Life. Version 0.41d
    New: Golly , a great new Game of Life program, has been released. (Get it? G ame O f L ife - ly Also, there has been a major redesign of this page on Feb. 19, 2007, but the content is pretty much the same, for now. Note to Firefox users on the Mac: Upgrade to version to fix the Java bugs. What is the Game of Life? Beginners should visit's Life Page Life is rich in terminology. If you don't know the meaning of a word that you find here, I encourage you to look it up in Stephen Silver's Life Lexicon On a historical note, here is the original article from the October 1970 issue of Scientific American which introduced the game to the public. Links for pattern hunters

    35. Cellular Automaton
    Fun introduction to cellular automata with interactive Java applets, including the game of life, a simulation of animal skin patterns and a screen saver.
    Fun with cellular automata
  • One-dimensional cellular automata Game of life Simulation of animal patterns Screen saver
  • Note: Your browser must have Java enabled to use the applets on these pages.
    One-dimensional cellular automata
    A cellular automaton is a group of cells that evolves only by nearest neighbor interaction. They are thought to be able to represent the evolution of living organisms and minerals. In one dimension, the cells are a line of points. Each point has a value, represented by a color. The evolution of each point is determined by its value and by the value of the neighboring points. By setting some simple rules for evolution, and picturing the evolution of the line of cells, it is possible to obtain very complex and beautiful patterns. Here are some examples giving an idea of the diversity of image that can result: In above examples, each point can take the values 0, 1, 2, or 3, corresponding respectively to the colors black, red, green, and blue. The initial state (i.e. the top line) is chosen randomly. Then, the cells evolve from top to bottom according to a set of rules, each line representing a step of evolution. How many rules are possible? If we consider only nearest neighbour interaction, and four colors, we have 4x4x4 = 64 different patterns possible of three cells. A rule of evolution is a function that relates each of these 64 patterns to one color. There are 4^64 patterns possible : it is a huge number, approximately 34000000000000000000000000000000000...

    36. Historical Notes: History Of Cellular Automata
    History of cellular automata. Despite their very simple construction, nothing like general cellular automata appear to have been considered before about the
    From: Stephen Wolfram, A New Kind of Science
    Notes for Chapter 2: The Crucial Experiment
    Section: Why These Discoveries Were Not Made Before
    History of cellular automata. Despite their very simple construction, nothing like general cellular automata appear to have been considered before about the 1950s. Yet in the 1950s - inspired in various ways by the advent of electronic computers - several different kinds of systems equivalent to cellular automata were independently introduced. A variety of precursors can be identified. Operations on sequences of digits had been used since antiquity in doing arithmetic. Finite difference approximations to differential equations began to emerge in the early 1900s and were fairly well known by the 1930s. And Turing machines invented in 1936 were based on thinking about arbitrary operations on sequences of discrete elements. (Notions in physics like the Ising model do not appear to have had a direct influence.)
    The best-known way in which cellular automata were introduced (and which eventually led to their name) was through work by John von Neumann in trying to develop an abstract model of self-reproduction in biology - a topic which had emerged from investigations in cybernetics. Around 1947 - perhaps based on chemical engineering - von Neumann began by thinking about models based on 3D factories described by partial differential equations. Soon he changed to thinking about robotics and imagined perhaps implementing an example using a toy construction set. By analogy to electronic circuit layouts he realized however that 2D should be enough. And following a 1951 suggestion from

    37. Cellular Automata - Wikibooks, Collection Of Open-content Textbooks
    This book aims to become a graduate to postgraduate level schoolbook on cellular automata. For those looking for a short informal introduction,
    Cellular Automata
    From Wikibooks, the open-content textbooks collection
    Jump to: navigation search This book aims to become a graduate to postgraduate level schoolbook on cellular automata. For those looking for a short informal introduction, see the Wikipedia page Cellular automaton
    edit Table of Contents
    Wikibook Development Stages Sparse text Developing text Maturing text Developed text Comprehensive text:
  • Introduction (August 8, 2005) Glossary (August 16, 2005) ... (October 20, 2005) Pattern Forward processing
  • Stephen Wolfram Classification Reverse processing (August 21, 2005)
  • Counting Preimages (August 16, 2005) ... (August 8, 2005) Statistical Analysis Information content
  • Information Dynamics (September 7, 2005) Information and Reversibility (September 7, 2005) Self Replication and Evolution Applications of Cellular Automata
  • Artificial Life Partial Differential Equations Fluid Dynamics (Lattice-Gas Cellular Automata) Excitable media (reaction-diffusion PDE) Image Processing (morphological operators) Examples
  • Examples on rule 110 (August 17, 2005) Examples of Plankton and Fish Dynamics ...
  • edit Notes for contributors
    • There is a sandbox for experimenting.

    38. Java Applets Collection
    cellular automata HOME PAGE
    Conway Life (squares) New gliders in the pentagonal and hexagonal grids Three dimensional life ...
    For more information, see Complex Systems 15 (2005) pp 245-252.

    visitors to this page since 10/10/04.

    39. Cellular Automata Pages At LIIN
    IFIP WG cellular automata and Machines home page. Resources on CA.
    The Cellular Automata Pages
    These are some WWW pages on Cellular Automata. If you have suggestions for improvements or additions, please let me know. Several people have already provided help; see the acknowledgements for a complete list.
    Workshop on Cellular Automata
    The workshop AUTOMATA 2007 will take place in Toronto (Canada) August 27-29, 2007 2007 (organized by A. Lawniczak and H. Fuks). The workshop AUTOMATA 2008 will take place in Bristol (UK) (organized by A. Adamatzky). The conference ACRI 2008 will take place in Yokohama (Japan), (most probably) September 23-26, 2008 (organized by H. Umeo,S. Morishita, K. Nishinari).
    IFIP Working Group 1.5
    The home page of the IFIP Working Group 1.5 on Cellular Automata and Machines.
    This list includes packages for the simulation of CA as well as packages which are useful e.g. for viewing the space of configurations for a certain rule or doing statistics.
    Interesting Links

    40. The Math Forum - Math Library - Cellular Automata
    The Math Forum s Internet Math Library is a comprehensive catalog of Web sites and Web pages relating to the study of mathematics. This page contains sites
    Browse and Search the Library
    Math Topics Dynamical Systems : Cellular Automata

    Library Home
    Search Full Table of Contents Suggest a Link ... Library Help
    Selected Sites (see also All Sites in this category
  • Cellular Automata Dynamics - Rafael Espericueta
    Explorations of 0-, 1-, and 2-dimensional cellular automata; and applications of cellular automata to ecosystem modeling. A slide show of the table of contents of the book is available here, as well as the full text of the book, in pdf format. more>>
  • The Game of Life: (Serendip: Complex Systems) - Bryn Mawr College
    Order without a planner: play a Java game about a world consisting of locations that may or may not be occupied by life. At each step, life persists in any location where it is also present in two or three of the eight neighboring locations, and otherwise disappears (from loneliness or overcrowding). Life is born in any empty location for which there is life in three of the eight neighboring locations. What would life look like in such a world? Would it die out? Persist as a disordered, ever-changing blob? Create stable, discrete entities? Generate particular forms in the absence of a planner, an architect, a blueprint? Does it matter what the starting conditions are? With thanks to John Conway. more>>
  • Mirek's Cellebration: 1D and 2D Cellular Automata explorer - Mirek Wojtowicz
    A large (120+) collection of 1D and 2D Cellular Automata. The site includes a lexicon, gallery, pattern of the week, CA families, rules, patterns, and links, with a CA tutorial and art. Also free Windows and Java software running all listed rules. The original site in Poland is at
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