1. 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.

2. Cellular Automata And The Edge Of Chaos David J. Eck s Javaillustrated introduction to 1-dimensional cellular automata. 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).)

3. Cellular Automata Reversible cellular automata, neighbourhoods, billiard ball machines, Java applets.By Tim Tyler. 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 [

4. Introduction To Cellular Automata Introduction to cellular automata illustrated by two programs. The text isavailable in PDF. 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 5 December, 2004

5. Five Cellular Automata Windows software implementing five cellular automata qstate Life, Belouzov-ZhabotinskyReaction, Togetherness, Viral Replication and Diffusion-Limited http://www.hermetic.ch/pca/pca.htm

Five Cellular Automata Introduction The five cellular automata: q-state Life The Belousov-Zhabotinsky Reaction Togetherness Viral Replication ... Upgrades 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.

6. Stephen Wolfram: Articles 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

Publications by Stephen Wolfram Articles Complete collection of Stephen Wolfram's classic articles from the 1970s and 1980s. General Interest Particle Physics General Physics Cosmology ... Technical Computing View all items listed by date Contact

7. 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://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

8. Cellular Automata Links cellular automata Links. cellular automata and Art Brian P. Hoke.cellular automata Digital Worlds - Alexander Schatten. An Introduction to Cellular 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

9. Stephen Wolfram Articles On Cellular Automata Stephen Wolfram Articles on cellular automata cellular automata as Simple SelfOrganizing Systems (1982) http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

10. Algorithms Archive A collection including searching, sorting, tracking, mathematics and cellular automata. In English and Italian. http://editor.altervista.org/

11. Cellular Automata Miscellanea A repository with cellular automata related papers, lectures and softwareconcentrating on Rule 110 by Harold V. McIntosh. http://delta.cs.cinvestav.mx/~mcintosh/

12. Cellular Automata An introduction to the history and properties of 1D and 2D cellular automata. http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

13. About Cellular Automata Onedimensional cellular automata. A one-dimensional cellular automaton (There are also two-dimensional cellular automata, which use rectangular grids 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.

14. Sandpiles In Graphs An application of cellular automata by Angela R. Kerns. http://www.cs.wvu.edu/~angela/cs418a/cs418a.html

Next: Introduction: Sandpiles in Graphs Sandpiles in Graphs Angela R. Kerns Department of Statistics and Computer Science West Virginia University angela@cs.wvu.edu Introduction: Sandpiles in Graphs Cellular Automata Models of Real Sandpiles The Basic Sandpile Model The Graph ... About this document ... Angela Kerns Thu Dec 5 15:22:37 EST 1996

15. The Primordial Soup Kitchen Colorful images and Java movies of cellular automata, with recipes to explain their genesis. Also some tasty Real Recipes. By David Griffeath. http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

16. Cellular Automaton -- From MathWorld cellular automata were studied in the early 1950s as a possible model for biological cellular automata come in a variety of shapes and varieties. http://mathworld.wolfram.com/CellularAutomaton.html

INDEX Algebra Applied Mathematics Calculus and Analysis Discrete Mathematics ... Alphabetical Index DESTINATIONS About MathWorld About the Author Headline News ... Random Entry CONTACT Contribute an Entry Send a Message to the Team MATHWORLD - IN PRINT Order book from Amazon Discrete Mathematics Cellular Automata Discrete Mathematics ... Commands Cellular Automaton A cellular automaton is a collection of "colored" cells on a grid of specified shape that evolves through a number of discrete time steps according to a set of rules based on the states of neighboring cells. The rules are then applied iteratively for as many time steps as desired. von Neumann was one of the first people to consider such a model, and incorporated a cellular model into his "universal constructor." Cellular automata were studied in the early 1950s as a possible model for biological systems (Wolfram 2002, p. ). Comprehensive studies of cellular automata have been performed by S. Wolfram starting in the 1980s, and Wolfram's fundamental research in the field culminated in the publication of his book A New Kind of Science (Wolfram 2002) in which Wolfram presents a gigantic collection of results concerning automata, among which are a number of groundbreaking new discoveries.

17. 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

18. Mirek's Cellebration - 1-D And 2-D Cellular Automata Viewer Mirek's Cellebration, 1D and 2-D cellular automata viewer, explorer and editor http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

19. Elementary Cellular Automaton -- From MathWorld The simplest class of onedimensional cellular automata. Elementary cellularautomata have two possible values for each cell (0 or 1), and rules that depend http://mathworld.wolfram.com/ElementaryCellularAutomaton.html

INDEX Algebra Applied Mathematics Calculus and Analysis Discrete Mathematics ... Alphabetical Index DESTINATIONS About MathWorld About the Author Headline News ... Random Entry CONTACT Contribute an Entry Send a Message to the Team MATHWORLD - IN PRINT Order book from Amazon Discrete Mathematics Cellular Automata Recreational Mathematics ... Mathematical Images Elementary Cellular Automaton The simplest class of one-dimensional cellular automata . Elementary cellular automata have two possible values for each cell (0 or 1), and rules that depend only on nearest neighbor values. As a result, the evolution of an elementary cellular automaton can completely be described by a table specifying the state a given cell will have in the next generation based on the value of the cell to its left, the value the cell itself, and the value of the cell to its right. Since there are possible binary states for the three cells neighboring a given cell, there are a total of elementary cellular automata, each of which can be indexed with an 8-bit binary number (Wolfram 1983, 2002). For example, the table giving the evolution of rule 30==000111102 is illustrated above. In this diagram, the possible values of the three neighboring cells are shown in the top row of each panel, and the resulting value the central cell takes in the next generation is shown below in the center.

20. Cellular Automata A Java applet demonstrating cellular automata models of cardiac dynamics; by Gil Bub. 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

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