1. Cellular Automata And The Edge Of Chaos cellular automata. And the Edge of Chaos type of automaton that has received a lot of attention is cellular automata. For one thing, they make pretty pictures http://math.hws.edu/xJava/CA

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).)

2. Cellular Automata Laboratory An extendable DOS/Windows application for exploring cellular automata, accompanied by a thorough user guide; by Rudy Rucker and John Walker. http://www.fourmilab.ch/cellab/

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.

3. Stephen Wolfram: Articles On Cellular Automata cellular automata. Stephen Wolfram Articles on cellular automata. Cellular Automaton Supercomputing ( 1988) Note Since 1987 Stephen Wolfram's intellectual efforts. have primarily been described in http://www.stephenwolfram.com/publications/articles/ca

Articles Cellular Automata Stephen Wolfram: Articles on Cellular Automata Cellular Automata as Simple Self-Organizing Systems 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.

4. Cellular Automata cellular automata. cellular automata are discrete dynamical systems whose behaviour is completely specified in terms of a local relation. http://www.brunel.ac.uk/depts/AI/alife/al-ca.htm

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. Mirek's Cellebration, 1D And 2D Cellular Automata Viewer, Editor And Explorer A collection of information relating to cellular automata. http://www.mirwoj.opus.chelm.pl/

6. EvCA Main Page Welcome to the Evolving cellular automata (EvCA) group home page! genetic algorithms are used to evolve cellular automata to perform computational tasks that require global http://www.santafe.edu/~evca

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. Evolving cellular automata with genetic algorithms Computational mechanics Population dynamics Coevolution 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.

7. 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. http://www.collidoscope.com/modernca/

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. 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 Site files: News Map Words

8. Artificial Life - Cellular Automata. cellular automata. New Conway's life in Flash. To go with this section I have created a mini version of conway's life. Click here to launch. . The father of cellular automata, and aLife come to that, is John von Neumann. one that can do this. A cellular automata is an array of 'cells' that interact with http://www.webslave.dircon.co.uk/alife/cellular.html

Cellular Automata New: Conway's life in Flash. To go with this section I have created a mini version of conway's life. Click here to launch. The father of Cellular Automata , and aLife come to that, is John von Neumann. He was the first to propose a system for producing life like results from simple rules. His aim was self reproduction; a John von Neumann machine is one that can do this. A cellular automata is an array of 'cells' that interact with their neighbors. These arrays can take on any number of dimensions, starting from a one dimensional string of cells. Each cell has its own State that can be a variable, property or other information. By receiving input from connected cells or general messages a cell uses its own set of rules to determine what its reaction should be. This reaction is a change of state and can also be a trigger to send out its own messages. These messages are passed onto other selected cells which cause them to act like wise. Natural cells work much in the same way. For example in an embryo messages are spread by timed releases of chemicals by cells which tell a cell which type of cell it should be. Each cell has a look up library, the code of DNA, to control its actions. A cell also has a chemical plant and chemical responses that act as its input and output devices. These plants are controlled by RNA, the slaves of DNA. Different doses of chemicals and in different combinations cause a cell to act in different ways. Sometime small changes in chemical density can lead to radical changes in cell formation. This is how cell barriers are formed. By a mixture of co-operation and competition complex forms, like a human baby, can be built up.

9. Cellular Automata cellular automata. Reversible cellular automata. Introduction to reversible automata. cellular automata optimisation. Definition of cellular automata. http://cell-auto.com/

var image_directory = "lib/tree/images/"; Cellular automata Reversible cellular automata Introduction to reversible automata Designing reversible automata Billiard ball machines Isometric cellular systems ... 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 [

10. Java CA Applet Christopher Osborn's Java applet exploring selfreproducing patterns. http://ourworld.compuserve.com/homepages/cdosborn/

This page has been moved to my new site at www.softrise.co.uk Please e-mail me if you cannot find the page you are looking for. (Chris Osborn 18 th January 2002 mailto:cdosborn@compuserve.com

11. Stephen Wolfram: Articles And Reports Technical articles by one of the leading CA researchers, concerning both 1D and 2D cellular automata. http://www.wolfram.com/s.wolfram/articles/indices/ca.html

Articles General Interest Particle Physics General Physics ... Technical Computing View all items listed by date

12. Cellular Automata cellular automata Examples. The applet on this page is a simple Greenburg Hastings type cellular automaton (CA). In a CA, each cell http://www.cnd.mcgill.ca/bios/bub/CAs.html

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 gilbub@hotmail.com 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. RUN Neighbourhood=1, E=8, R=10, threshold=3

13. 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. http://www.rennard.org/alife/english/acgb.html

Introduction to Cellular Automata Cellular Automata Viewer CAV 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 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...). H ome Cellular Automata Biomorphs ... Links Last Update 23 March, 2003

14. Cellular Automata http://www.santafe.edu/~shalizi/notebooks/cellular-automata.html

Notebooks Cellular Automata 24 Dec 2003 17:04 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. transition rule, finite-state automaton cellular automaton, or CA. To run it, you colors the cells in your favorite pattern, start the clock, and stand back. neighborhood, any pattern of cells which will fill the plane One important use of CAs is to mimic bits and pieces of the real world, or, as they say in the trade, to model lattice gasses pattern formation , for insect colonies, for ecosystems , for the development of organisms CAs were not invented, however, to be realistic models of Nature. They started with John von Neumann , who wanted to study self-reproduction, and decided that the first thing to do was ignore everything biologists had learned about the way actually existing organisms reproduce themselves. This is known as hubris, Build a general constructive automaton, according this plan; Copy this tape into the new constructor, then you have an automaton (constructor + tape) which will reproduce itself.

15. Cellular Automata Links JCASim cellular automata simulation system. Java applet traffic simulation using CA. EDEVO - Synthesized Evolution using Self-Reproducing cellular automata. http://cell-auto.com/links/index.php

var image_directory = "../lib/tree/images/"; Links Java CA simulators Mirek's Java Cellebration - by Mirek Wojtowicz CSprings - (was WebsideCA) - a general Java CA explorer on the "Isle Ex" website JCASim: Cellular automata simulation system Java applet traffic simulation - using CA jTrend Other CA simulators Mirek's comprehensive list of simulators Mirek's Cellebration - by Mirek Wojtowicz SARCASIM - George Maydwell's Windows-based "Animation reduction" automata LifeMN - Windows CA explorer - by Ben Schaeffer CellLab - Windows - by Rudy Rucker and John Walker XToys - CAs for the X window system CAGE CAFUN An old list of simulators Langton-like loops Evolving self-replicating loops - C. D. Osborne (Java applet) SR CA - C. D. Osborne (Java application) Hu Hsien Chou and his life Hiroki Sayama Hiroki Sayama Sayama's Worms - Java applet EvoLoop and SDSR "Structurally-dissolving" self-replicating loops Various self-replicating loops - by Eli Bachmutsky (Java applet) Langton Loop (Java applet) "Langton-Sayama-Loop" (Java applet) Sayama's Evoloop (Java applet) Self-replication On a Chessboard (Java applet) Swiss self-reproducing automata (Java applet) EDEVO - Synthesized Evolution using Self-Reproducing Cellular Automata Dana Eckart's examples of CA - including a Langton loop Knowledge Engineering Knowledge Engineering (Japan) Keuichi Morita Cellular Automata Reversible Cellular Automata - with Satoshi Ueno Self-replicating Self-replicating Universal Reversible Partitioning Cellular Automata Rectangular ... 2D Hexagonal Reversible Partitioned Cellular Automata - PDF document

16. THE COMPUTATIONAL NOTION OF LIFE Claus EMMECHE, 1994. This paper makes an interesting link between concepts of computation, cellular automata and the definition of the concept of information. http://www.nbi.dk/~emmeche/cePubl/compnolife.html

published in Theoria - Segunda Epoca THE COMPUTATIONAL NOTION OF LIFE Claus EMMECHE "Where shall we find a machine that reproduces its own substance and at the same time grows, structures itself, reconstitutes itself upon trauma, reorganises itself in response to changes in its environments, and programmes its own reproduction?" ABSTRACT The present paper discusses a topic often neglected by contemporary philosophy of biology: The relation between metaphorical notions of living organisms as information processing systems, the attempts to model such systems by computational means (e.g., Artificial Life research), and the idea that life itself is a computational phenomenon. This question has ramifications in theoretical biology and the definition of life, in theoretical computer science and the concept of computation, and in semiotics (the study of signs in the most general sense, including information, signification, and meaning), and the concept of the interpreter. It is argued, that the theory of autopoietic systems known from theoretical biology should be integrated with a biosemiotic reflection on the natural history of signs. Introduction The title of the present paper perhaps seems a little obscure, so we will in a moment explain the idea of life as a computational phenomenon in relation to the study of artificial life. However, let us first consider term semiotics, i.e., the general study of signs and sign interpretation processes, and biosemiotics, the study of sign processes in living systems. The question to be addressed first is what constitutes the

17. About Cellular Automata Introdution to. Onedimensional cellular automata. A one-dimensional cellular automaton consists of two things a row of cells and a set of rules . http://math.hws.edu/xJava/CA/CA.html

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.

18. QuikCAT Technologies Specializing in data compression software technologies for wireless transmission, Internet acceleration, Microsoft Exchange and Lotus Notes Email acceleration, and PDA video conferencing, using cellular automata transforms. http://www.quikcat.com

Sitemap Search ::::::::: QuikCAT News :::::::::::::::: Products Miliki Super Compressor iNet Accelerator Messaging Optimizer CATNIP Technology Technology Patents Company About QuikCAT Job Opportunities Downloads File Reader Support iNet Care Feedback Contact Us Home Technologies is an industry leader providing efficient, secure and cost effective data delivery solutions. Technologies is focused on the development of applications for fast delivery of data across any network using applicable compression, data routing, caching and encryption technologies including schemes based on our patented Cellular Automata Transforms (CAT). Email Digital Photos,Microsoft Office documents and PDF files up to faster and save up to on disk space with Miliki Super Compressor.

19. Elementary Cellular Automaton From MathWorld Elementary Cellular Automaton from MathWorld The simplest class of onedimensional cellular automata. Elementary cellular automata have two possible values for each cell (0 or 1), and rules http://rdre1.inktomi.com/click?u=http://mathworld.wolfram.com/ElementaryCellular

20. Cellular Automata Laboratory Exploring cellular automata. by Rudy Rucker and John Walker. cellular automata Theory Neighbors; Vote and Other Totalistic Rules; Life; Brain; Semitotalistic Rules; http://www.fourmilab.ch/cellab/manual/

USER GUIDE Exploring Cellular Automata by Rudy Rucker and John Walker Table of Contents Introduction Getting Started What Are Cellular Automata? Overview of the Programs ... About this Edition

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