Modelling with Cellular Automata
Total Page:16
File Type:pdf, Size:1020Kb
Load more
Recommended publications
-
GNU/Linux AI & Alife HOWTO
GNU/Linux AI & Alife HOWTO GNU/Linux AI & Alife HOWTO Table of Contents GNU/Linux AI & Alife HOWTO......................................................................................................................1 by John Eikenberry..................................................................................................................................1 1. Introduction..........................................................................................................................................1 2. Symbolic Systems (GOFAI)................................................................................................................1 3. Connectionism.....................................................................................................................................1 4. Evolutionary Computing......................................................................................................................1 5. Alife & Complex Systems...................................................................................................................1 6. Agents & Robotics...............................................................................................................................1 7. Statistical & Machine Learning...........................................................................................................2 8. Missing & Dead...................................................................................................................................2 1. Introduction.........................................................................................................................................2 -
On Soliton Collisions Between Localizations in Complex ECA: Rules 54 and 110 and Beyond
On soliton collisions between localizations in complex ECA: Rules 54 and 110 and beyond Genaro J. Mart´ınez Departamento de Ciencias e Ingenier´ıade la Computaci´on, Escuela Superior de C´omputo,Instituto Polit´ecnico Nacional, M´exico Unconventional Computing Center, Computer Science Department, University of the West of England, Bristol BS16 1QY, United Kingdom genaro. martinez@ uwe. ac. uk Andrew Adamatzky Unconventional Computing Center, Computer Science Department, University of the West of England, Bristol BS16 1QY, United Kingdom andrew. adamatzky@ uwe. ac. uk Fangyue Chen School of Sciences, Hangzhou Dianzi University Hangzhou, Zhejiang 310018, P. R. China fychen@ hdu. edu. cn Leon Chua Electrical Engineering and Computer Sciences Department University of California at Berkeley, California, United States of America chua@ eecs. berkeley. edu In this paper we present a single-soliton two-component cellular au- tomata (CA) model of waves as mobile self-localizations, also known as: particles, waves, or gliders; and its version with memory. The model is based on coding sets of strings where each chain represents a unique mobile self-localization. We will discuss briefly the original soli- ton models in CA proposed with filter automata, followed by solutions in elementary CA (ECA) domain with the famous universal ECA Rule 110, and reporting a number of new solitonic collisions in ECA Rule 54. A mobile self-localization in this study is equivalent a single soliton because the collisions of these mobile self-localizations studied in this paper satisfies the property of solitonic collisions. We also present a arXiv:1301.6258v1 [nlin.CG] 26 Jan 2013 specific ECA with memory (ECAM), the ECAM Rule φR9maj:4, that displays single-soliton solutions from any initial codification (including random initial conditions) for a kind of mobile self-localization because such automaton is able to adjust any initial condition to soliton struc- tures. -
Universality of Evolved Cellular Automata In-Materio
Universality of Evolved Cellular Automata in-Materio STEFANO NICHELE12?,SIGVE SEBASTIAN FARSTAD1,GUNNAR TUFTE1 1 Department of Computer and Information Science, Norwegian University of Science and Technology, Norway 2 Department of Computer Science, Oslo and Akershus University College of Applied Sciences, Norway Received xxxxx; In final form xxxxx Evolution-in-Materio (EIM) is a method of using artificial evolu- tion to exploit physical properties of materials for computation. It has previously been successfully used to evolve a multitude of different computational devices implemented in physical ma- terials. One of the biggest problems in exploiting materials is finding a good computational abstraction to carry computation on top of the underlying physical process. This paper presents elementary cellular automata (CA) as a possible abstraction and presents successfully evolved CA transition functions in single- walled carbon nanotube (SWCNT) and polymer composite ma- terials. Such implementation allows reasoning about the compu- tational capabilities of materials and draw analogies with cellu- lar automata complexity and computation at the Edge of Chaos. This work is done within the European Project NASCENCE. Key words: Evolution-in-Materio, Cellular Automata, Edge of Chaos, Single-Walled Carbon Nanotubes, Complexity, Computational Materi- als. ? email: [email protected] 1 1 INTRODUCTION The natural evolutionary process, in stark contrast to the traditional human top-down building-block-oriented engineering approach, is not one of ab- straction, componentization and careful manipulation based on an under- standing of underlying mechanics. Rather, it is a ”blind-yet-guided” meta- heuristic approach able to exploit properties to create ”designs” without need- ing to understand them or the underlying mechanics that power them. -
Think Complexity: Exploring Complexity Science in Python
Think Complexity Version 2.6.2 Think Complexity Version 2.6.2 Allen B. Downey Green Tea Press Needham, Massachusetts Copyright © 2016 Allen B. Downey. Green Tea Press 9 Washburn Ave Needham MA 02492 Permission is granted to copy, distribute, transmit and adapt this work under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License: https://thinkcomplex.com/license. If you are interested in distributing a commercial version of this work, please contact the author. The LATEX source for this book is available from https://github.com/AllenDowney/ThinkComplexity2 iv Contents Preface xi 0.1 Who is this book for?...................... xii 0.2 Changes from the first edition................. xiii 0.3 Using the code.......................... xiii 1 Complexity Science1 1.1 The changing criteria of science................3 1.2 The axes of scientific models..................4 1.3 Different models for different purposes............6 1.4 Complexity engineering.....................7 1.5 Complexity thinking......................8 2 Graphs 11 2.1 What is a graph?........................ 11 2.2 NetworkX............................ 13 2.3 Random graphs......................... 16 2.4 Generating graphs........................ 17 2.5 Connected graphs........................ 18 2.6 Generating ER graphs..................... 20 2.7 Probability of connectivity................... 22 vi CONTENTS 2.8 Analysis of graph algorithms.................. 24 2.9 Exercises............................. 25 3 Small World Graphs 27 3.1 Stanley Milgram......................... 27 3.2 Watts and Strogatz....................... 28 3.3 Ring lattice........................... 30 3.4 WS graphs............................ 32 3.5 Clustering............................ 33 3.6 Shortest path lengths...................... 35 3.7 The WS experiment....................... 36 3.8 What kind of explanation is that?............... 38 3.9 Breadth-First Search..................... -
Automatic Detection of Interesting Cellular Automata
Automatic Detection of Interesting Cellular Automata Qitian Liao Electrical Engineering and Computer Sciences University of California, Berkeley Technical Report No. UCB/EECS-2021-150 http://www2.eecs.berkeley.edu/Pubs/TechRpts/2021/EECS-2021-150.html May 21, 2021 Copyright © 2021, by the author(s). All rights reserved. Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. To copy otherwise, to republish, to post on servers or to redistribute to lists, requires prior specific permission. Acknowledgement First I would like to thank my faculty advisor, professor Dan Garcia, the best mentor I could ask for, who graciously accepted me to his research team and constantly motivated me to be the best scholar I could. I am also grateful to my technical advisor and mentor in the field of machine learning, professor Gerald Friedland, for the opportunities he has given me. I also want to thank my friend, Randy Fan, who gave me the inspiration to write about the topic. This report would not have been possible without his contributions. I am further grateful to my girlfriend, Yanran Chen, who cared for me deeply. Lastly, I am forever grateful to my parents, Faqiang Liao and Lei Qu: their love, support, and encouragement are the foundation upon which all my past and future achievements are built. Automatic Detection of Interesting Cellular Automata by Qitian Liao Research Project Submitted to the Department of Electrical Engineering and Computer Sciences, University of California at Berkeley, in partial satisfaction of the requirements for the degree of Master of Science, Plan II. -
Conway's Game of Life
Conway’s Game of Life Melissa Gymrek May 2010 Introduction The Game of Life is a cellular-automaton, zero player game, developed by John Conway in 1970. The game is played on an infinite grid of square cells, and its evolution is only determined by its initial state. The rules of the game are simple, and describe the evolution of the grid: ◮ Birth: a cell that is dead at time t will be alive at time t + 1 if exactly 3 of its eight neighbors were alive at time t. ◮ Death: a cell can die by: ◮ Overcrowding: if a cell is alive at time t +1 and 4 or more of its neighbors are also alive at time t, the cell will be dead at time t + 1. ◮ Exposure: If a live cell at time t has only 1 live neighbor or no live neighbors, it will be dead at time t + 1. ◮ Survival: a cell survives from time t to time t +1 if and only if 2 or 3 of its neighbors are alive at time t. Starting from the initial configuration, these rules are applied, and the game board evolves, playing the game by itself! This might seem like a rather boring game at first, but there are many remarkable facts about this game. Today we will see the types of “life-forms” we can create with this game, whether we can tell if a game of Life will go on infinitely, and see how a game of Life can be used to solve any computational problem a computer can solve. -
Investigation of Elementary Cellular Automata for Reservoir Computing
Investigation of Elementary Cellular Automata for Reservoir Computing Emil Taylor Bye Master of Science in Computer Science Submission date: June 2016 Supervisor: Stefano Nichele, IDI Norwegian University of Science and Technology Department of Computer and Information Science Summary Reservoir computing is an approach to machine learning. Typical reservoir computing approaches use large, untrained artificial neural networks to transform an input signal. To produce the desired output, a readout layer is trained using linear regression on the neural network. Recently, several attempts have been made using other kinds of dynamic systems in- stead of artificial neural networks. Cellular automata are an example of a dynamic system that has been proposed as a replacement. This thesis attempts to discover whether cellular automata are a viable candidate for use in reservoir computing. Four different tasks solved by other reservoir computing sys- tems are attempted with elementary cellular automata, a limited subset of all possible cellular automata. The effect of changing different properties of the cellular automata are investigated, and the results are compared with the results when performing the same experiments with typical reservoir computing systems. Reservoir computing seems like a potentially very interesting utilization of cellular automata. However, it is evident that more research into this field is necessary to reach performance comparable to existing reservoir computing systems. i ii Acknowledgements I would like to express my very great appreciation to my supervisor, Dr. Stefano Nichele. His insights, guidance and encouragement has proven invaluable and vital to the comple- tion of this thesis. I would also like to offer my special thanks to Solveig Isabel Taylor, who apart from being an excellent proofreader, also did a marvelous job at helping me search for literature. -
Interview with John Horton Conway
Interview with John Horton Conway Dierk Schleicher his is an edited version of an interview with John Horton Conway conducted in July 2011 at the first International Math- ematical Summer School for Students at Jacobs University, Bremen, Germany, Tand slightly extended afterwards. The interviewer, Dierk Schleicher, professor of mathematics at Jacobs University, served on the organizing com- mittee and the scientific committee for the summer school. The second summer school took place in August 2012 at the École Normale Supérieure de Lyon, France, and the next one is planned for July 2013, again at Jacobs University. Further information about the summer school is available at http://www.math.jacobs-university.de/ summerschool. John Horton Conway in August 2012 lecturing John H. Conway is one of the preeminent the- on FRACTRAN at Jacobs University Bremen. orists in the study of finite groups and one of the world’s foremost knot theorists. He has written or co-written more than ten books and more than one- received the Pólya Prize of the London Mathemati- hundred thirty journal articles on a wide variety cal Society and the Frederic Esser Nemmers Prize of mathematical subjects. He has done important in Mathematics of Northwestern University. work in number theory, game theory, coding the- Schleicher: John Conway, welcome to the Interna- ory, tiling, and the creation of new number systems, tional Mathematical Summer School for Students including the “surreal numbers”. He is also widely here at Jacobs University in Bremen. Why did you known as the inventor of the “Game of Life”, a com- accept the invitation to participate? puter simulation of simple cellular “life” governed Conway: I like teaching, and I like talking to young by simple rules that give rise to complex behavior. -
Evolution of Autopoiesis and Multicellularity in the Game of Life
Evolution of Autopoiesis and Peter D. Turney* Ronin Institute Multicellularity in the Game of Life [email protected] Keywords Evolution, autopoiesis, multicellularity, Abstract Recently we introduced a model of symbiosis, Model-S, cellular automata, diversity, symbiosis based on the evolution of seed patterns in Conwayʼs Game of Life. In the model, the fitness of a seed pattern is measured by one-on-one competitions in the Immigration Game, a two-player variation of the Downloaded from http://direct.mit.edu/artl/article-pdf/27/1/26/1925167/artl_a_00334.pdf by guest on 25 September 2021 Game of Life. Our previous article showed that Model-S can serve as a highly abstract, simplified model of biological life: (1) The initial seed pattern is analogous to a genome. (2) The changes as the game runs are analogous to the development of the phenome. (3) Tournament selection in Model-S is analogous to natural selection in biology. (4) The Immigration Game in Model-S is analogous to competition in biology. (5) The first three layers in Model-S are analogous to biological reproduction. (6) The fusion of seed patterns in Model-S is analogous to symbiosis. The current article takes this analogy two steps further: (7) Autopoietic structures in the Game of Life (still lifes, oscillators, and spaceships—collectively known as ashes) are analogous to cells in biology. (8) The seed patterns in the Game of Life give rise to multiple, diverse, cooperating autopoietic structures, analogous to multicellular biological life. We use the apgsearch software (Ash Pattern Generator Search), developed by Adam Goucher for the study of ashes, to analyze autopoiesis and multicellularity in Model-S. -
Cellular Automata
Cellular Automata Dr. Michael Lones Room EM.G31 [email protected] ⟐ Genetic programming ▹ Is about evolving computer programs ▹ Mostly conventional GP: tree, graph, linear ▹ Mostly conventional issues: memory, syntax ⟐ Developmental GP encodings ▹ Programs that build other things ▹ e.g. programs, structures ▹ Biologically-motivated process ▹ The developed programs are still “conventional” forwhile + 9 WRITE ✗ 2 3 1 i G0 G1 G2 G3 G4 ✔ ⟐ Conventional ⟐ Biological ▹ Centralised ▹ Distributed ▹ Top-down ▹ Bottom-up (emergent) ▹ Halting ▹ Ongoing ▹ Static ▹ Dynamical ▹ Exact ▹ Inexact ▹ Fragile ▹ Robust ▹ Synchronous ▹ Asynchronous ⟐ See Mitchell, “Biological Computation,” 2010 http://www.santafe.edu/media/workingpapers/10-09-021.pdf ⟐ What is a cellular automaton? ▹ A model of distributed computation • Of the sort seen in biology ▹ A demonstration of “emergence” • complex behaviour emerges from Stanislaw Ulam interactions between simple rules ▹ Developed by Ulam and von Neumann in the 1940s/50s ▹ Popularised by John Conway’s work on the ‘Game of Life’ in the 1970s ▹ Significant later work by Stephen Wolfram from the 1980s onwards John von Neumann ▹ Stephen Wolfram, A New Kind of Science, 2002 ▹ https://www.wolframscience.com/nksonline/toc.html ⟐ Computation takes place on a grid, which may have 1, 2 or more dimensions, e.g. a 2D CA: ⟐ At each grid location is a cell ▹ Which has a state ▹ In many cases this is binary: State = Off State = On ⟐ Each cell contains an automaton ▹ Which observes a neighbourhood around the cell ⟐ Each cell contains -
Complexity Properties of the Cellular Automaton Game of Life
Portland State University PDXScholar Dissertations and Theses Dissertations and Theses 11-14-1995 Complexity Properties of the Cellular Automaton Game of Life Andreas Rechtsteiner Portland State University Follow this and additional works at: https://pdxscholar.library.pdx.edu/open_access_etds Part of the Physics Commons Let us know how access to this document benefits ou.y Recommended Citation Rechtsteiner, Andreas, "Complexity Properties of the Cellular Automaton Game of Life" (1995). Dissertations and Theses. Paper 4928. https://doi.org/10.15760/etd.6804 This Thesis is brought to you for free and open access. It has been accepted for inclusion in Dissertations and Theses by an authorized administrator of PDXScholar. Please contact us if we can make this document more accessible: [email protected]. THESIS APPROVAL The abstract and thesis of Andreas Rechtsteiner for the Master of Science in Physics were presented November 14th, 1995, and accepted by the thesis committee and the department. COMMITTEE APPROVALS: 1i' I ) Erik Boaegom ec Representativi' of the Office of Graduate Studies DEPARTMENT APPROVAL: **************************************************************** ACCEPTED FOR PORTLAND STATE UNNERSITY BY THE LIBRARY by on /..-?~Lf!c-t:t-?~~ /99.s- Abstract An abstract of the thesis of Andreas Rechtsteiner for the Master of Science in Physics presented November 14, 1995. Title: Complexity Properties of the Cellular Automaton Game of Life The Game of life is probably the most famous cellular automaton. Life shows all the characteristics of Wolfram's complex Class N cellular automata: long-lived transients, static and propagating local structures, and the ability to support universal computation. We examine in this thesis questions about the geometry and criticality of Life. -
Universality in Elementary Cellular Automata
Universality in Elementary Cellular Automata Matthew Cook Department of Computation and Neural Systems,! Caltech, Mail Stop 136-93, Pasadena, California 91125, USA The purpose of this paper is to prove a conjecture made by Stephen Wolfram in 1985, that an elementary one dimensional cellular automaton known as “Rule 110” is capable of universal computation. I developed this proof of his conjecture while assisting Stephen Wolfram on research for A New Kind of Science [1]. 1. Overview The purpose of this paper is to prove that one of the simplest one di- mensional cellular automata is computationally universal, implying that many questions concerning its behavior, such as whether a particular se- quence of bits will occur, or whether the behavior will become periodic, are formally undecidable. The cellular automaton we will prove this for is known as “Rule 110” according to Wolfram’s numbering scheme [2]. Being a one dimensional cellular automaton, it consists of an infinitely long row of cells "Ci # i $ !%. Each cell is in one of the two states "0, 1%, and at each discrete time step every cell synchronously updates ' itself according to the value of itself and its nearest neighbors: &i, Ci ( F(Ci)1, Ci, Ci*1), where F is the following function: F(0, 0, 0) ( 0 F(0, 0, 1) ( 1 F(0, 1, 0) ( 1 F(0, 1, 1) ( 1 F(1, 0, 0) ( 0 F(1, 0, 1) ( 1 F(1, 1, 0) ( 1 F(1, 1, 1) ( 0 This F encodes the idea that a cell in state 0 should change to state 1 exactly when the cell to its right is in state 1, and that a cell in state 1 should change to state 0 just when the cells on both sides are in state 1.