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41. Elementary Cellular Automaton -- From Wolfram MathWorld
The simplest class of onedimensional cellular automata. Elementary cellular automata have two possible values for each cell (0 or 1), and rules that depend only on nearest
http://mathworld.wolfram.com/ElementaryCellularAutomaton.html
 Algebra Applied Mathematics Calculus and Analysis Discrete Mathematics ... Interactive Demonstrations 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 ) 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. generations of elementary cellular automaton rule are implemented as CellularAutomaton r n All All The evolution of a one-dimensional cellular automaton can be illustrated by starting with the initial state (generation zero) in the first row, the first generation on the second row, and so on. For example, the figure above illustrated the first 20 generations of the

 42. 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..http://www.stewdean.com/alife/cellular.html

43. Isle Ex: Transmusic: Cellular Automaton Music
Music samples generated using some popular cellular automata rules; by John Elliott.
http://jmge.net/camusic.htm
 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.

44. Cellular Automata
Dec 19, 1995 Contents Resources Nonlinear dynamics Cellular automata Lindenmeyer systems (L systems) Finite state machines von Neumann machines Adapt
http://www.aridolan.com/ad/adb/ca.html
Home Page Alife Database (Main Menu) Home Page
##### Cellular Automata
Artificial Life A Message from the Editors If you haven't done so already, please take a few seconds to go to the Splash Page and read about the renovations going on here at Alife Online. We realize that many users have this page bookmarked, not that one, but because of the construction currently underway, we strongly advise changing your bookmarks to point at http://alife.santafe.edu/index.html, and not this pa Artificial Life Software Artificial Life software Much of the software listed here is also available via anonymous ftp at alife.santafe.edu. Unix JVN: An implementation of the John von Neumann Universal Constructor (R. Nobili and U. Pesavento) Netlife: evolving neural nets in an environment (Christopher Busch) Primoridal Soup: an artificial life system that spontaneously generates self-reproducing organisms from a steril Artificial life links Artificial life links Java Applets for Neural Network and Artificial Life Applets for Neural Networks and Artificial Life (To Japanese version) Contents Competitive Learning Backpropagation Learning Neural Nets for Constraint Satisfaction and Optimization Other Neural Networks Artificial Life Other Related Applets Simulated Annealing, Cellular Automaton, Bayesian Network, Turing Machine, etc. Competitive Learning Vector Quantizer (VQ) Related to hard competitive learni Links to online papers on Self-Organisation, Complexity and Artificial Life compiled by CALResCo

45. Life-like Cellular Automaton - Wikipedia, The Free Encyclopedia
Twodimensional cellular automata . Journal of Statistical Physics 38 901–946. doi 10.1007/BF01010423. Reprinted in Cellular Automata and Complexity, pp. 211–249.
http://en.wikipedia.org/wiki/Life-like_cellular_automaton
##### Life-like cellular automaton
From Wikipedia, the free encyclopedia Jump to: navigation search A cellular automaton (CA) is Life-like (in the sense of being similar to Conway's Game of Life ) if it meets the following criteria:
• The CA has two dimensions. The CA has two states (called OFF and ON). The neighborhood is the Moore neighborhood ; it consists of the eight adjacent cells to the one under consideration and (possibly) the cell itself. The new state of the cell in the next generation can be expressed as a function of the number of adjacent cells that are in the ON state and the cell's own state; that is, the rule is outer totalistic (sometimes called semitotalistic
This class of cellular automata is named for the Game of Life (B3/S23), the most famous cellular automaton. Many different terms are used to describe this class. It is common to refer to it as the "Life family" or to simply use phrases like "similar to Life".
##### edit Notation for rules
There are three standard notations for describing these rules, that are similar to each other but incompatible.

46. Xtoys
A set of Cellular Automata simulators written for XWindows. By Mike Creutz.
http://quark.phy.bnl.gov/www/xtoys/xtoys.html
##### Xtoys
This page is about a set of cellular automata simulators I have written for the xwindow system. The xtoys gallery shows lots of pictures produced by these programs (beware if you have a slow link). To peek at the xising user interface, look here A further description of these files is in my contribution to the Lattice'95 proceedings. The files in the xtoys directory include:

 47. Grant Robinson : Cellular Automata Launcher I was inspired to make these small apps after reading Emergence The Connected Lives of Ants, Brains, Cities, and Software by Steven Johnson (a great readhttp://grant.robinson.name/projects/cellularAutomata/

48. Cellular Automata Software, Including Multistate Game Of Life
Windows software implementing five cellular automata q-state Life, Belouzov-Zhabotinsky Reaction, Togetherness, Viral Replication and Diffusion-Limited Aggregation; by Hermetic Systems.
http://www.hermetic.ch/pca/pca.htm
 Five Cellular Automata Five Cellular Automata is a program for exploring five cellular automata. One of these is a generalization of Conway's Game of Life to a multistate cellular automaton (rather than one with just two states). Three of these cellular automata are simulations of chemical or biological processes, and another is related to simulation of physical processes as done in computational physics. The algorithms for each of these cellular automata are described in detail. 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 The five cellular automata: q-state Life The Belousov-Zhabotinsky Reaction Togetherness Viral Replication ... Algorithms 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:

49. Homepage Alexander Schatten - Information / Tutorials
A cellular automata tutorial that covers the structure, behaviour and some applications of CA and offers a philosophical background as well; by Alexander Schatten.
http://www.schatten.info/info/ca/ca.html
Homepage Alexander Schatten - Information / Tutorials Home
Contact/CV

Information/Tutorials
Lehre/Forschung

Main Interests

Software

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

 50. Visions Of Chaos Home page of a versatile Windows software by Jason Rampe. The program covers Cellular Automata, Chaos, and Fractals.http://www.softology.com.au/voc.htm

51. Mirek's Java Cellebration
Mar 16, 2002 Mirek s Java Cellebration (MJCell) is a Java applet that allows playing 300+ Cellular Automata rules and 1400+ patterns.
http://psoup.math.wisc.edu/mcell/mjcell/mjcell.html
##### Mirek's Java Cellebration v.1.50 what's new?
Go back to MCell Home Mirek's Java Cellebration (MJCell) is a Java applet that allows playing 300+ Cellular Automata rules and 1400+ patterns. It can play rules from 13 CA rules families: Generations Life Vote Weighted Life ... Larger than Life , and some of the User DLLs . It allows also to experiment with own rules. The applet is a simplified version of MCell. It does not offer extended features of MCell, but has one advantage over it: its usage is not restricted to MS Windows. Full source code of the applet is available here . You can also download the full off-line version equipped in a rich library of patterns. You should also download this version if you plan to put the MJCell applet on your own Web page. To start the applet, click on the "Start" button below. The applet will show up in its own window. For the description of all rules available in the applet refer to the CA rules page Sign my MJCell GuestBook Read my MJCell GuestBook
[ GuestBook by TheGuestBook.com

52. FADarchitecture (Francis Bitonti)
Last tested with Processing 1.0 Keywords Cellular Automata, Algorithm Last Update Jan/01/09 EXAMPLES (ZIP FILE) DOWNLOAD_SOURCE (GOOGLE CODE)
http://cellularautomata.fadarch.com/
FADarch is the experimental design and research entity for Francis Anthony Bitonti. FADarch is also dedicated to the research and application of computational technologies such as algorithmic design methodologies and robotics to architectural design and construction. Francis A. Bitonti is an architect and designer based in New York. Francis holds a Masters of Architecture from Pratt Institute and a BFA from Long Island University in Digital Media. Francis founded FADarch in 2007 as an experimental design and research entity. In addition to his work with FADarch Francis has been a visiting instructor at Pratt Institute in the Graduate Architecture and Urban Design department (GAUD).
##### _Publications/Exhibitions
Exhibition: Cooper-Hewitt National Design Museum: on display October 2008
Lecture given at the University of Indiana
NKS Midwest Conference 2008
Exhibition: (F.U.E.L. Collection) Philadelphia PA.
Published in: Manifold Magazine Issue 2 This page is currently under construction more projects will be posted soon.

53. Discrete Dynamics Lab
Tools for researching discrete dynamical networks - from cellular automata to random boolean networks; by Andrew Wuensche.
http://www.ddlab.com/
Discrete Dynamics Lab HOME PAGE
Tools for researching Cellular Automata, Random Boolean Networks, multi-value Discrete Dynamical Networks, and beyond
##### Andy Wuensche
andy AT ddlab DOT org
Visiting research fellow

Dept. of Informatics (formerly COGS)
School of Science and Technology, University of Sussex International Center of Unconventional Computing
University of the West of England DDLab mirror sites:
www.cogs.susx.ac.uk/users/andywu/ddlab.html

uncomp.uwe.ac.uk/wuensche/ddlab.html

www.ddlab.org

DDLab is no longer hosted at SFI as of July 2003. xxx
to support the DDLab project LINKS 3d-glider-guns New features Lecture slides DD-Life ... Thesis Latest DDLab and NEW MANUAL work-in-progress June 2010 The latest DDLab and its new manual are available as work-in-progress. DDLab has many improvements and bug fixes at present Linux, Cygwin, Mac and DOS versions are available. The new manual is revised up to chapter 30. 3134 are still as the old manual, 35 is updated, 36 is new but unfinished. Updates will be posted at regular intervals.
• Download DDLab (about 0.5 MB):

54. Discrete, Amorphous Physical Models - Cellular Automata, Physics, Models Of Comp
Minimal discrete models. Cellular automata-like animations without grids or synchronization; by Erik Rauch.
http://swiss.csail.mit.edu/~rauch/dapm/
##### How minimal can a discrete model be?
Discrete models of physical phenomena are an attractive alternative to continuous models such as partial differential equations. In discrete models, such as cellular automata, space is treated as having finitely many locations per unit volume and time is discrete, whereas continuous models (e.g. Schroedinger's equation, and most field theories) specify detail down to infinitesimal spatial and time scales. But all existing discrete models depend critically on a regular (crystalline) lattice, as well as the global synchronization of all sites. We should ask, on the grounds of minimalism, whether the global synchronization and regular lattice are inherent in any discrete formulation. Is it possible to do without these conditions and still have a useful physical model? Or are they somehow fundamental?
Transcript (with slides) of invited talk
given at the NSF Digital Perspectives on Physics workshop, July 25, 2001
Discrete, Amorphous Physical Models

 55. Wonders Of Math - The Game Of Life There has been much recent interest in cellular automata, a field of mathematical research. Life is one of the simplest cellular automata to have beenhttp://www.math.com/students/wonders/life/life.html

 56. Cellular Automata File Format PDF/Adobe Acrobat Quick Viewhttp://www.dagstuhl.de/Reports/95/9510.pdf

57. CELLULAR AUTOMATA
by A Ilachinski Cited by 265 - Related articles
http://www.worldscibooks.com/chaos/4702.html
 Search Home Join Our Mailing List New Reviews New Titles ... E-Catalogues NONLINEAR SCIENCE All Nonlinear Science Titles New Titles September Bestsellers Editor's Choice ... Book Series Related Journals Advances in Complex Systems (ACS) Fractals Nonlinear Science Journals Request for related catalogues PRODUCTS Journals eBooks Journals Archives eProceedings RESOURCES Print flyer Full Version Condensed Version Recommend title Request for Inspection copy ... News CELLULAR AUTOMATA A Discrete Universe by Andrew Ilachinski (Center for Naval Analyses, USA) Table of Contents Foreword Preface Chapter 1: Introduction: Preliminary Musings Cellular automata are a class of spatially and temporally discrete mathematical systems characterized by local interaction and synchronous dynamical evolution. Introduced by the mathematician John von Neumann in the 1950s as simple models of biological self-reproduction, they are prototypical models for complex systems and processes consisting of a large number of simple, homogeneous, locally interacting components. Cellular automata have been the focus of great attention over the years because of their ability to generate a rich spectrum of very complex patterns of behavior out of sets of relatively simple underlying rules. Moreover, they appear to capture many essential features of complex self-organizing cooperative behavior observed in real systems. This book provides a summary of the basic properties of cellular automata, and explores in depth many important cellular-automata-related research areas, including artificial life, chaos, emergence, fractals, nonlinear dynamics, and self-organization. It also presents a broad review of the speculative proposition that cellular automata may eventually prove to be theoretical harbingers of a fundamentally new information-based, discrete physics. Designed to be accessible at the junior/senior undergraduate level and above, the book will be of interest to all students, researchers, and professionals wanting to learn about order, chaos, and the emergence of complexity. It contains an extensive bibliography and provides a listing of cellular automata resources available on the World Wide Web.

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

59. Cellular Automata « Random (Blog)
May 19, 2010 Cellular automata are simulations on a linear, square, or cubic grid on which each cell can be in a single state, often just ON and OFF,
http://nbickford.wordpress.com/2010/05/19/cellular-automata/
Random (Blog)
##### Cellular Automata
Cellular automata are simulations on a linear, square, or cubic grid on which each cell can be in a single state, often just ON and OFF, and where each cell operates on its own, taking the states of its neighbors as input and showing a state as output. One of the simplest examples of these would be a 1-dimensional cellular automaton in which each cell has two states, ON and OFF, which are represented by black and white, and where each cell turns on if at least one of its neighbors are in the ON state. When started from 1 cell, this simply creates a widening black line. When the layers are shown all at once, though, you can see that it makes a pyramidal shape. All layers at once Stephen Wolfram developed a numbering system for all cellular automata which base only on themselves, their left-hand neighbor, and their right-hand neighbor, often called the elementary cellular automata, which looks something like this for the Sierpinski Triangle automata (Rule 18): This code has all possible ON and OFF states for three cells on the top, and the effect that it creates on the cell below them on the bottom. Using this system, we can find that there are 256 different elementary cellular automata. We can also easily create a number for each automaton by simply converting the ON and OFF states at the bottom to 1s and 0s, and then combining them to make a binary number (00010010 in the Sierpinski Triangle example). Then, we convert the binary to decimal and so get the rule number. (128*0+64*0+32*0+16*1+8*0+4*0+2*1+1*0= 18 for the example).  We can also do the reverse to get a cellular automata from a number. Using this method, we can create pictures of all 255 elementary cellular automata:

60. Dr.Cell Cellular Automata Simulator
A tool for simulating uniform or non-uniform cellular automata for a variety of neighborhood models, implemented in Scheme (a dialect of Lisp) using PLT s Dr.Scheme.
http://student.vub.ac.be/~nkaraogl/drcell/drcell.htm
 Dr.Cell Cellular Automata Simulator Dr.Cell is a CA simulation tool implemented in Scheme programming language (a dialect of Lisp) using PLT's Dr.Scheme Dr.Cell allows you to simulate 1D, 2D, Uniform and Non-Uniform Cellular Automata graphically with user defined neighborhood models and rule sets. Following are a few samples that are implemented using Dr.Cell: You can load simulations using the Cellular Universe Control Center and execute multiple simulations at the same time. For each simulation there will be an individual window (Cellular World) showing the graphic representation of the simulation along with the cell statistics. Once a cellular world is created you can add more "automata" (Artificial Life Forms) on to the world and see their interactions. For example you can create a world for "Carrots" containing a specific rule set for the "Carrots". Then you may define another life-form "Rabbits" with the rule set for rabbits and add it to the "carrot world" and see how carrot and rabbit population evaluating in time. Dr.Cell allows you to adjust the speed of a simulation. You can also stop a simulation at any given time and execute it step by step.

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