Game Of Life Cellular Automata

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Game of Life Cellular Automata

Author : Andrew Adamatzky
Publisher : Springer Science & Business Media
Page : 579 pages
File Size : 47,9 Mb
Release : 2010-06-14
Category : Computers
ISBN : 9781849962179

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Game of Life Cellular Automata by Andrew Adamatzky Pdf

In the late 1960s British mathematician John Conway invented a virtual mathematical machine that operates on a two-dimensional array of square cell. Each cell takes two states, live and dead. The cells’ states are updated simultaneously and in discrete time. A dead cell comes to life if it has exactly three live neighbours. A live cell remains alive if two or three of its neighbours are alive, otherwise the cell dies. Conway’s Game of Life became the most programmed solitary game and the most known cellular automaton. The book brings together results of forty years of study into computational, mathematical, physical and engineering aspects of The Game of Life cellular automata. Selected topics include phenomenology and statistical behaviour; space-time dynamics on Penrose tilling and hyperbolic spaces; generation of music; algebraic properties; modelling of financial markets; semi-quantum extensions; predicting emergence; dual-graph based analysis; fuzzy, limit behaviour and threshold scaling; evolving cell-state transition rules; localization dynamics in quasi-chemical analogues of GoL; self-organisation towards criticality; asynochrous implementations. The volume is unique because it gives a comprehensive presentation of the theoretical and experimental foundations, cutting-edge computation techniques and mathematical analysis of the fabulously complex, self-organized and emergent phenomena defined by incredibly simple rules.

Game of Life Cellular Automata

Author : Andrew Adamatzky
Publisher : Springer
Page : 579 pages
File Size : 42,6 Mb
Release : 2011-03-25
Category : Computers
ISBN : 1849962189

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Game of Life Cellular Automata by Andrew Adamatzky Pdf

In the late 1960s British mathematician John Conway invented a virtual mathematical machine that operates on a two-dimensional array of square cell. Each cell takes two states, live and dead. The cells’ states are updated simultaneously and in discrete time. A dead cell comes to life if it has exactly three live neighbours. A live cell remains alive if two or three of its neighbours are alive, otherwise the cell dies. Conway’s Game of Life became the most programmed solitary game and the most known cellular automaton. The book brings together results of forty years of study into computational, mathematical, physical and engineering aspects of The Game of Life cellular automata. Selected topics include phenomenology and statistical behaviour; space-time dynamics on Penrose tilling and hyperbolic spaces; generation of music; algebraic properties; modelling of financial markets; semi-quantum extensions; predicting emergence; dual-graph based analysis; fuzzy, limit behaviour and threshold scaling; evolving cell-state transition rules; localization dynamics in quasi-chemical analogues of GoL; self-organisation towards criticality; asynochrous implementations. The volume is unique because it gives a comprehensive presentation of the theoretical and experimental foundations, cutting-edge computation techniques and mathematical analysis of the fabulously complex, self-organized and emergent phenomena defined by incredibly simple rules.

The Recursive Universe

Author : William Poundstone
Publisher : Courier Corporation
Page : 258 pages
File Size : 53,8 Mb
Release : 2013-06-19
Category : Science
ISBN : 9780486490984

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The Recursive Universe by William Poundstone Pdf

This fascinating popular science journey explores key concepts in information theory in terms of Conway's "Game of Life" program. The author explains the application of natural law to a random system and demonstrates the necessity of limits. Other topics include the limits of knowledge, paradox of complexity, Maxwell's demon, Big Bang theory, and much more. 1985 edition.

Turing Machine Universality of the Game of Life

Author : Paul Rendell
Publisher : Springer
Page : 177 pages
File Size : 44,7 Mb
Release : 2015-07-21
Category : Technology & Engineering
ISBN : 9783319198422

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Turing Machine Universality of the Game of Life by Paul Rendell Pdf

This book presents a proof of universal computation in the Game of Life cellular automaton by using a Turing machine construction. It provides an introduction including background information and an extended review of the literature for Turing Machines, Counter Machines and the relevant patterns in Conway's Game of Life so that the subject matter is accessibly to non specialists. The book contains a description of the author’s Turing machine in Conway’s Game of Life including an unlimited storage tape provided by growing stack structures and it also presents a fast universal Turing machine designed to allow the working to be demonstrated in a convenient period of time.

Collision-Based Computing

Author : Andrew Adamatzky
Publisher : Springer Science & Business Media
Page : 588 pages
File Size : 47,8 Mb
Release : 2002-05-13
Category : Computers
ISBN : 1852335408

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Collision-Based Computing by Andrew Adamatzky Pdf

Collision-Based Computing presents a unique overview of computation with mobile self-localized patterns in non-linear media, including computation in optical media, mathematical models of massively parallel computers, and molecular systems. It covers such diverse subjects as conservative computation in billiard ball models and its cellular-automaton analogues, implementation of computing devices in lattice gases, Conway's Game of Life and discrete excitable media, theory of particle machines, computation with solitons, logic of ballistic computing, phenomenology of computation, and self-replicating universal computers. Collision-Based Computing will be of interest to researchers working on relevant topics in Computing Science, Mathematical Physics and Engineering. It will also be useful background reading for postgraduate courses such as Optical Computing, Nature-Inspired Computing, Artificial Intelligence, Smart Engineering Systems, Complex and Adaptive Systems, Parallel Computation, Applied Mathematics and Computational Physics.

Designing Beauty: The Art of Cellular Automata

Author : Andrew Adamatzky,Genaro J. Martínez
Publisher : Springer
Page : 191 pages
File Size : 41,8 Mb
Release : 2016-01-05
Category : Technology & Engineering
ISBN : 9783319272702

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Designing Beauty: The Art of Cellular Automata by Andrew Adamatzky,Genaro J. Martínez Pdf

This fascinating, colourful book offers in-depth insights and first-hand working experiences in the production of art works, using simple computational models with rich morphological behaviour, at the edge of mathematics, computer science, physics and biology. It organically combines ground breaking scientific discoveries in the theory of computation and complex systems with artistic representations of the research results. In this appealing book mathematicians, computer scientists, physicists, and engineers brought together marvelous and esoteric patterns generated by cellular automata, which are arrays of simple machines with complex behavior. Configurations produced by cellular automata uncover mechanics of dynamic patterns formation, their propagation and interaction in natural systems: heart pacemaker, bacterial membrane proteins, chemical rectors, water permeation in soil, compressed gas, cell division, population dynamics, reaction-diffusion media and self-organisation. The book inspires artists to take on cellular automata as a tool of creativity and it persuades scientists to convert their research results into the works of art. The book is lavishly illustrated with visually attractive examples, presented in a lively and easily accessible manner.

The Grapes of Math

Author : Alex Bellos
Publisher : Simon and Schuster
Page : 352 pages
File Size : 46,6 Mb
Release : 2014-06-10
Category : Mathematics
ISBN : 9781451640120

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The Grapes of Math by Alex Bellos Pdf

From triangles, rotations and power laws, to cones, curves and the dreaded calculus, Alex takes you on a journey of mathematical discovery with his signature wit and limitless enthusiasm. He sifts through over 30,000 survey submissions to uncover the world’s favourite number, and meets a mathematician who looks for universes in his garage. He attends the World Mathematical Congress in India, and visits the engineer who designed the first roller-coaster loop. Get hooked on math as Alex delves deep into humankind’s turbulent relationship with numbers, and reveals how they have shaped the world we live in.

Cellular Automata

Author : Alejandro Salcido
Publisher : BoD – Books on Demand
Page : 584 pages
File Size : 54,7 Mb
Release : 2011-04-11
Category : Computers
ISBN : 9789533072302

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Cellular Automata by Alejandro Salcido Pdf

Cellular automata make up a class of completely discrete dynamical systems, which have became a core subject in the sciences of complexity due to their conceptual simplicity, easiness of implementation for computer simulation, and their ability to exhibit a wide variety of amazingly complex behavior. The feature of simplicity behind complexity of cellular automata has attracted the researchers' attention from a wide range of divergent fields of study of science, which extend from the exact disciplines of mathematical physics up to the social ones, and beyond. Numerous complex systems containing many discrete elements with local interactions have been and are being conveniently modelled as cellular automata. In this book, the versatility of cellular automata as models for a wide diversity of complex systems is underlined through the study of a number of outstanding problems using these innovative techniques for modelling and simulation.

New Constructions in Cellular Automata

Author : David Griffeath,Cristopher Moore
Publisher : Oxford University Press
Page : 364 pages
File Size : 42,7 Mb
Release : 2003-03-27
Category : Science
ISBN : 0198031394

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New Constructions in Cellular Automata by David Griffeath,Cristopher Moore Pdf

This book not only discusses cellular automata (CA) as accouterment for simulation, but also the actual building of devices within cellular automata. CA are widely used tools for simulation in physics, ecology, mathematics, and other fields. But they are also digital "toy universes" worthy of study in their own right, with their own laws of physics and behavior. In studying CA for their own sake, we must look at constructive methods, that is the practice of actually building devices in a given CA that store and process in formation, replicate, and propagate themselves, and interact with other devices in complex ways. By building such machines, we learn what the CA's dynamics are capable of, and build an intuition about how to "engineer" the machine we want. We can also address fundamental questions, such as whether universal computation or even "living" things that reproduce and evolve can exist in the CA's digital world, and perhaps, how these things came to be in out own universe.

Cellular Automata

Author : M. Delorme,J. Mazoyer
Publisher : Springer Science & Business Media
Page : 394 pages
File Size : 52,8 Mb
Release : 1998-12-31
Category : Computers
ISBN : 0792354931

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Cellular Automata by M. Delorme,J. Mazoyer Pdf

Cellular automata can be viewed both as computational models and modelling systems of real processes. This volume emphasises the first aspect. In articles written by leading researchers, sophisticated massive parallel algorithms (firing squad, life, Fischer's primes recognition) are treated. Their computational power and the specific complexity classes they determine are surveyed, while some recent results in relation to chaos from a new dynamic systems point of view are also presented. Audience: This book will be of interest to specialists of theoretical computer science and the parallelism challenge.

Cellular Automata and Groups

Author : Tullio Ceccherini-Silberstein,Michel Coornaert
Publisher : Springer Science & Business Media
Page : 440 pages
File Size : 43,5 Mb
Release : 2010-08-24
Category : Computers
ISBN : 9783642140341

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Cellular Automata and Groups by Tullio Ceccherini-Silberstein,Michel Coornaert Pdf

Cellular automata were introduced in the first half of the last century by John von Neumann who used them as theoretical models for self-reproducing machines. The authors present a self-contained exposition of the theory of cellular automata on groups and explore its deep connections with recent developments in geometric group theory, symbolic dynamics, and other branches of mathematics and theoretical computer science. The topics treated include in particular the Garden of Eden theorem for amenable groups, and the Gromov-Weiss surjunctivity theorem as well as the solution of the Kaplansky conjecture on the stable finiteness of group rings for sofic groups. The volume is entirely self-contained, with 10 appendices and more than 300 exercises, and appeals to a large audience including specialists as well as newcomers in the field. It provides a comprehensive account of recent progress in the theory of cellular automata based on the interplay between amenability, geometric and combinatorial group theory, symbolic dynamics and the algebraic theory of group rings which are treated here for the first time in book form.

The Nature of Code

Author : Daniel Shiffman
Publisher : No Starch Press
Page : 0 pages
File Size : 44,6 Mb
Release : 2024-09-03
Category : Computers
ISBN : 9781718503717

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The Nature of Code by Daniel Shiffman Pdf

All aboard The Coding Train! This beginner-friendly creative coding tutorial is designed to grow your skills in a fun, hands-on way as you build simulations of real-world phenomena with “The Coding Train” YouTube star Daniel Shiffman. How can we use code to capture the unpredictable properties of nature? How can understanding the mathematical principles behind our physical world help us create interesting digital environments? Written by “The Coding Train” YouTube star Daniel Shiffman, The Nature of Code is a beginner-friendly creative coding tutorial that explores a range of programming strategies for developing computer simulations of natural systems—from elementary concepts in math and physics to sophisticated machine-learning algorithms. Using the same enthusiastic style on display in Shiffman’s popular YT channel, this book makes learning to program fun, empowering you to generate fascinating graphical output while refining your problem-solving and algorithmic-thinking skills. You’ll progress from building a basic physics engine that simulates the effects of forces like gravity and wind resistance, to creating evolving systems of intelligent autonomous agents that can learn from their mistakes and adapt to their environment. The Nature of Code introduces important topics such as: Randomness Forces and vectors Trigonometry Cellular automata and fractals Genetic algorithms Neural networks Learn from an expert how to transform your beginner-level skills into writing well-organized, thoughtful programs that set the stage for further experiments in generative design. NOTE: All examples are written with p5.js, a JavaScript library for creative coding, and are available on the book's website.

Simulating Complex Systems by Cellular Automata

Author : Alfons G. Hoekstra,Jiri Kroc,Peter M.A. Sloot
Publisher : Springer Science & Business Media
Page : 392 pages
File Size : 53,8 Mb
Release : 2010-06-13
Category : Computers
ISBN : 9783642122026

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Simulating Complex Systems by Cellular Automata by Alfons G. Hoekstra,Jiri Kroc,Peter M.A. Sloot Pdf

Deeply rooted in fundamental research in Mathematics and Computer Science, Cellular Automata (CA) are recognized as an intuitive modeling paradigm for Complex Systems. Already very basic CA, with extremely simple micro dynamics such as the Game of Life, show an almost endless display of complex emergent behavior. Conversely, CA can also be designed to produce a desired emergent behavior, using either theoretical methodologies or evolutionary techniques. Meanwhile, beyond the original realm of applications - Physics, Computer Science, and Mathematics – CA have also become work horses in very different disciplines such as epidemiology, immunology, sociology, and finance. In this context of fast and impressive progress, spurred further by the enormous attraction these topics have on students, this book emerges as a welcome overview of the field for its practitioners, as well as a good starting point for detailed study on the graduate and post-graduate level. The book contains three parts, two major parts on theory and applications, and a smaller part on software. The theory part contains fundamental chapters on how to design and/or apply CA for many different areas. In the applications part a number of representative examples of really using CA in a broad range of disciplines is provided - this part will give the reader a good idea of the real strength of this kind of modeling as well as the incentive to apply CA in their own field of study. Finally, we included a smaller section on software, to highlight the important work that has been done to create high quality problem solving environments that allow to quickly and relatively easily implement a CA model and run simulations, both on the desktop and if needed, on High Performance Computing infrastructures.

Cellular Automata Transforms

Author : Olurinde Lafe
Publisher : Springer
Page : 177 pages
File Size : 40,6 Mb
Release : 2000-08-31
Category : Computers
ISBN : 0792378571

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Cellular Automata Transforms by Olurinde Lafe Pdf

Cellular Automata Transforms describes a new approach to using the dynamical system, popularly known as cellular automata (CA), as a tool for conducting transforms on data. Cellular automata have generated a great deal of interest since the early 1960s when John Conway created the `Game of Life'. This book takes a more serious look at CA by describing methods by which information building blocks, called basis functions (or bases), can be generated from the evolving states. These information blocks can then be used to construct any data. A typical dynamical system such as CA tend to involve an infinite possibilities of rules that define the inherent elements, neighborhood size, shape, number of states, and modes of association, etc. To be able to build these building blocks an elegant method had to be developed to address a large subset of these rules. A new formula, which allows for the definition a large subset of possible rules, is described in the book. The robustness of this formula allows searching of the CA rule space in order to develop applications for multimedia compression, data encryption and process modeling. Cellular Automata Transforms is divided into two parts. In Part I the fundamentals of cellular automata, including the history and traditional applications are outlined. The challenges faced in using CA to solve practical problems are described. The basic theory behind Cellular Automata Transforms (CAT) is developed in this part of the book. Techniques by which the evolving states of a cellular automaton can be converted into information building blocks are taught. The methods (including fast convolutions) by which forward and inverse transforms of any data can be achieved are also presented. Part II contains a description of applications of CAT. Chapter 4 describes digital image compression, audio compression and synthetic audio generation, three approaches for compressing video data. Chapter 5 contains both symmetric and public-key implementation of CAT encryption. Possible methods of attack are also outlined. Chapter 6 looks at process modeling by solving differential and integral equations. Examples are drawn from physics and fluid dynamics.

Cellular Automata Machines

Author : Tommaso Toffoli,Norman Margolus
Publisher : MIT Press
Page : 284 pages
File Size : 46,5 Mb
Release : 1987
Category : Computers
ISBN : 0262200600

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Cellular Automata Machines by Tommaso Toffoli,Norman Margolus Pdf

Theory of Computation -- Computation by Abstracts Devices.