FAKULT¨AT F¨UR INFORMATIK Probabilistic Cellular Automata
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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. -
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. -
Dipl. Eng. Thesis
A Framework for the Real-Time Execution of Cellular Automata on Reconfigurable Logic By NIKOLAOS KYPARISSAS Microprocessor & Hardware Laboratory School of Electrical & Computer Engineering TECHNICAL UNIVERSITY OF CRETE A thesis submitted to the Technical University of Crete in accordance with the requirements for the DIPLOMA IN ELECTRICAL AND COMPUTER ENGINEERING. FEBRUARY 2020 THESIS COMMITTEE: Prof. Apostolos Dollas, Technical University of Crete, Thesis Supervisor Prof. Dionisios Pnevmatikatos, National Technical University of Athens Prof. Michalis Zervakis, Technical University of Crete ABSTRACT ellular automata are discrete mathematical models discovered in the 1940s by John von Neumann and Stanislaw Ulam. They constitute a general paradigm for massively parallel Ccomputation. Through time, these powerful mathematical tools have been proven useful in a variety of scientific fields. In this thesis we propose a customizable parallel framework on reconfigurable logic which can be used to efficiently simulate weighted, large-neighborhood totalistic and outer-totalistic cellular automata in real time. Simulating cellular automata rules with large neighborhood sizes on large grids provides a new aspect of modeling physical processes with realistic features and results. In terms of performance results, our pipelined application-specific architecture successfully surpasses the computation and memory bounds found in a general-purpose CPU and has a measured speedup of up to 51 against an Intel Core i7-7700HQ CPU running highly optimized £ software programmed in C. i ΠΕΡΙΛΗΨΗ α κυψελωτά αυτόματα είναι διακριτά μαθηματικά μοντέλα που ανακαλύφθηκαν τη δεκαετία του 1940 από τον John von Neumann και τον Stanislaw Ulam. Αποτελούν ένα γενικό Τ υπόδειγμα υπολογισμών με εκτενή παραλληλισμό. Μέχρι σήμερα τα μαθηματικά αυτά εργαλεία έχουν χρησιμεύσει σε πληθώρα επιστημονικών τομέων. -
Asymptotic Densities for Packard Box Rules Janko Gravner Mathematics
Asymptotic densities for Packard Box rules Janko Gravner Mathematics Department University of California Davis, CA 95616 e-mail: [email protected] David Griffeath Department of Mathematics University of Wisconsin Madison, WI 53706 e-mail: [email protected] (Revised version, February 2009) Abstract. This paper studies two-dimensional totalistic solidification cellular automata with Moore neighborhood such that a single occupied neighbor is sufficient for a site to join the occupied set. We focus on asymptotic density of the final configuration, obtaining rigorous results mainly in cases with an additive component. When sites with two occupied neighbors also solidify, additivity yields a comprehensive result for general finite initial sets. In particular, the density is independent of the seed. More generally, analysis is restricted to special initializations, cases with density 1, and various experimental findings. In the case that requires either one or three occupied neighbors for solidification, we show that different seeds may produce many different densities. For each of two particularly common densities we present a scheme that recognizes a seed in its domain of attraction. 2000 Mathematics Subject Classification. Primary 37B15. Secondary 68Q80, 11B05. Keywords: additive dynamics, asymptotic density, cellular automaton, growth model. Acknowledgments. Experimental aspects of this research were conducted by a Collaborative Undergraduate Research Lab (CURL) at the University of Wisconsin-Madison Mathematics Department during the 2006–7 academic year. The CURL was sponsored by a National Science Foundation VIGRE award. We are particularly grateful to lab participants Charles D. Brummitt and Chad Koch for empirical analysis of the Box 12 rule. Support. JG was partially supported by NSF grant DMS–0204376 and the Republic of Slove- nia’s Ministry of Science program P1-285. -
Controls on Video Rental Eased
08120 A RETAILER'S L, GUIDE TO HO-ME NEWSPAPER BB049GREENL YMDNT00 t4AR83 MONTY GREENLY 03 1 C UCY 3740 ELM LONG BEACH CA 90807 A Billboard Publication w & w Entertainment The International Newsweekly Of Music Home Aug. 28, 1982 $3 (U.S.) VIA FOUR CHAINS Controls On Video Rental Eased Impact Of Price Cut On Less Rental -Only Titles; Warner Drops `Choice' Plan Tapes Tested At Retail By LAURA FOTI shows how rental -only plans have The "B" and "lease /purchase" been revised and what effect the re- classifications have been dropped. By JOHN SIPF EL LOS ANGELES major Key retail executives at NEW YORK -Major studios are visions are having at retail. The "Dealer's Choice" program -Four con.inually. retail chains hope to prove for man- the meeting, however, also com- fast relinquishing control over home Warner Home Video, for ex- was instituted in January, after a na- that dramatically lower mer_ted that LPs' decline in numbers video rental programs. More and ample, has dropped its "Dealer's tional outcry against the original ufacturers list prices on prerecorded tape can at tLe sales register is not being com- more, dealers are selling or renting at Choice" program, with its three -tier Warner Home Video rental -only increase sales. pensated for by the cassettes' their option regardless of restrictions title classification and lease /pur- plan launched in October, 1981. The substantially Single Camelot, Tower, Western growth. imposed when product was ac- chase plan. While the company still revised version was said by dealers Merchandising and Flipside (Chi- (Continued on page 15) quired, with little or no interference has rental -only titles, their release to be extremely complex, although it stores are currently carrying from manufacturers. -
Symbiosis Promotes Fitness Improvements in the Game of Life
Symbiosis Promotes Fitness Peter D. Turney* Ronin Institute Improvements in the [email protected] Game of Life Keywords Symbiosis, cooperation, open-ended evolution, Game of Life, Immigration Game, levels of selection Abstract We present a computational simulation of evolving entities that includes symbiosis with shifting levels of selection. Evolution by natural selection shifts from the level of the original entities to the level of the new symbiotic entity. In the simulation, the fitness of an entity is measured by a series of one-on-one competitions in the Immigration Game, a two-player variation of Conwayʼs Game of Life. Mutation, reproduction, and symbiosis are implemented as operations that are external to the Immigration Game. Because these operations are external to the game, we can freely manipulate the operations and observe the effects of the manipulations. The simulation is composed of four layers, each layer building on the previous layer. The first layer implements a simple form of asexual reproduction, the second layer introduces a more sophisticated form of asexual reproduction, the third layer adds sexual reproduction, and the fourth layer adds symbiosis. The experiments show that a small amount of symbiosis, added to the other layers, significantly increases the fitness of the population. We suggest that the model may provide new insights into symbiosis in biological and cultural evolution. 1 Introduction There are two main definitions of symbiosis in biology, (1) symbiosis as any association and (2) symbiosis as persistent mutualism [7]. The first definition allows any kind of persistent contact between different species of organisms to count as symbiosis, even if the contact is pathogenic or parasitic. -
Carle's Game: an Open-Ended Challenge in Exploratory Machine
Carle’s Game: An Open-Ended Challenge in Exploratory Machine Creativity 1st Q. Tyrell Davis Wyoming, USA [email protected] Abstract—This paper is both an introduction and an invitation. understand the context of Earth-based intelligence as it fits It is an introduction to CARLE, a Life-like cellular automata into the larger universe. simulator and reinforcement learning environment. It is also an One hallmark of modern approaches to artificial intelligence invitation to Carle’s Game, a challenge in open-ended machine exploration and creativity. Inducing machine agents to excel at (AI), particularly in a reinforcement learning framework, is creating interesting patterns across multiple cellular automata the ability of learning agents to exploit unintended loopholes universes is a substantial challenge, and approaching this chal- in the way a task is specified [1]. Known as specification lenge is likely to require contributions from the fields of artificial gaming or reward hacking, this tendency constitutes the crux life, AI, machine learning, and complexity, at multiple levels of of the control problem and places an additional engineering interest. Carle’s Game is based on machine agent interaction with CARLE, a Cellular Automata Reinforcement Learning Environ- burden of designing an “un-hackable” reward function, the ment. CARLE is flexible, capable of simulating any of the 262,144 substantial effort of which may defeat the benefits of end- different rules defining Life-like cellular automaton universes. to-end learning [43]. An attractive alternative to manually CARLE is also fast and can simulate automata universes at a rate specifying robust and un-exploitable rewards is to instead of tens of thousands of steps per second through a combination of develop methods for intrinsic or learned rewards [4]. -
Emergence from Symmetry: a New Type of Cellular Automata
Emergence from Symmetry: A New Type of Cellular Automata Zan Pan ∗ Department of Modern Physics, University of Science and Technology of China, Hefei, 230026, P. R. China Abstract In the realm of cellular automata (CA), Conway’s Game of Life (Life) has gained the most fondness, due to its striking simplicity of rules but an impressive diversity of behavior. Based on it, a large family of models were investigated, e.g. Seeds, Replicator, Larger than Life, etc. They all inherit key ideas from Life, determining a cell’s state in the next generation by counting the number of its current living neighbors. In this paper, a different perspective of constructing the CA models is proposed. Its kernel, the Local Symmetric Distribution Principle, relates to some fundamental concepts in physics, which maybe raise a wide interest. With a rich palette of configurations, this model also hints its capability of universal computation. Moreover, it possesses a general tendency to evolve towards certain symmetrical directions. Some illustrative examples are given and physical interpretations are discussed in depth. To measure the evolution’s fluctuating between order and chaos, three parameters are introduced, i.e. order parameter, complexity index and entropy. In addition, we focus on some particular simulations and giving a brief list of open problems as well. 1 Introduction The conception of cellular automaton (CA) stems from John von Neumann’s research on self-replicating artificial systems with computational universality [22]. However, it was John Horton Conway’s fas- cinating Game of Life (Life) [15, 8] which simplified von Neumann’s ideas that greatly enlarged its influence among scientists. -
Cellular Automata
Cellular Automata Orit Moskovich 4.12.2013 Outline ´ What is a Cellular Automaton? ´ Wolfram’s Elementary CA ´ Conway's Game of Life ´ Applications and Summary Cellular automaton ´ A discrete model ´ Regular grid of cells, each in one of a finite number of states ´ The grid can be in any finite number of dimensions ´ For each cell, a set of cells called its neighborhood is defined relative to the specified cell Moore von Neumann neighborhood neighborhood Cellular automaton ´ An initial state (time t=0) is selected by assigning a state for each cell ´ A new generation is created (advancing t by 1), according to some fixed rule that determines the new state of each cell in terms of: ´ the current state of the cell ´ the states of the cells in its neighborhood ´ Typically, the rule set is ´ the same for each cell Moore von Neumann ´ does not change over time neighborhood neighborhood ´ applied to the whole grid simultaneously Background Ulam ´ Originally discovered in the 1940s by Stanislaw Ulam and John von Neumann ´ Ulam was studying the growth of crystals and von Neumann was imagining a world of self-replicating robots ´ Studied by some throughout the 1950s and 1960s ´ Conway's Game of Life (1970), a two-dimensional cellular automaton, interest in the subject expanded beyond academia von Neumann ´ In the 1980s, Stephen Wolfram engaged in a systematic study of one- dimensional cellular automata (elementary cellular automata) ´ Wolfram’s research assistant Matthew Cook showed that one of these rules has a VERY cool and important property ´ Wolfram published A New Kind of Science in 2002 and discusses how CA are not simply cool, but are relevant to the study of many fields in science, such as biology, chemistry, physics, computer processors and cryptography, and many more Why the big interest??? ´ A complex system, generated from a very simple configuration ´ Is this even possible? ´ Cellular automata can simulate a variety of real-world systems. -
Searching for Spaceships
More Games of No Chance MSRI Publications Volume 42, 2002 Searching for Spaceships DAVID EPPSTEIN Abstract. We describe software that searches for spaceships in Conway's Game of Life and related two-dimensional cellular automata. Our program searches through a state space related to the de Bruijn graph of the automa- ton, using a method that combines features of breadth first and iterative deepening search, and includes fast bit-parallel graph reachability and path enumeration algorithms for finding the successors of each state. Successful results include a new 2c=7 spaceship in Life, found by searching a space with 2126 states. 1. Introduction John Conway's Game of Life has fascinated and inspired many enthusiasts, due to the emergence of complex behavior from a very simple system. One of the many interesting phenomena in Life is the existence of gliders and spaceships: small patterns that move across space. When describing gliders, spaceships, and other early discoveries in Life, Martin Gardner wrote (in 1970) that spaceships \are extremely hard to find” [10]. Very small spaceships can be found by human experimentation, but finding larger ones requires more sophisticated methods. Can computer software aid in this search? The answer is yes { we describe here a program, gfind, that can quickly find large low-period spaceships in Life and many related cellular automata. Among the interesting new patterns found by gfind are the \weekender" 2c=7 spaceship in Conway's Life (Figure 1, right), the \dragon" c=6 Life spaceship found by Paul Tooke (Figure 1, left), and a c=7 spaceship in the Diamoeba rule (Figure 2, top). -
Fifty Years of Research on Self-Replication: an Overview
Fifty Years of Research on Moshe Sipper Logic Systems Laboratory Self-Replication: An Overview Swiss Federal Institute of Technology IN-Ecublens CH-1015 Lausanne Switzerland [email protected]fl.ch http://lslwww.epfl.ch/ Abstract The study of artificial self-replicating structures or moshes machines has been taking place now for almost half a » century. My goal in this article is to present an overview of research carried out in the domain of self-replication over the past 50 years, starting from von Neumann’s work in the late 1940s and continuing to the most recent research efforts. I Keywords shall concentrate on computational models, that is, ones that self-replication, cellular automata, self-replicating programs, self-repli- have been studied from a computer science point of view, be cating strings, self-replicating ma- it theoretical or experimental. The systems are divided into chines four major classes, according to the model on which they are based: cellular automata, computer programs, strings (or strands), or an altogether different approach. With the advent of new materials, such as synthetic molecules and nanomachines, it is quite possible that we shall see this somewhat theoretical domain of study producing practical, real-world applications. 1 Introduction In the late 1940s eminent mathematician and physicist John von Neumann had become interested in the question of whether a machine can self-replicate, that is, produce copies of itself. Von Neumann wished to investigate the logic necessary for replication— he was not interested in, nor did he have the tools for, building a working machine at the biochemical or genetic level. -
Lattice-Gas Cellular Automata and Lattice Boltzmann Models - an Introduction
Dieter A. Wolf-Gladrow Alfred Wegener Institute for Polar and Marine Research, Postfach 12 01 61 D-27515 Bremerhaven Germany e-mail: [email protected] Version 1.05 Lattice-Gas Cellular Automata and Lattice Boltzmann Models - An Introduction June 26, 2005 Springer Berlin Heidelberg NewYork Hong Kong London Milan Paris Tokyo Contents 1 Introduction ............................................... -1 1.1 Preface ................................................ 0 1.2 Overview............................................... 2 1.3 The basic idea of lattice-gas cellular automata and lattice Boltzmannmodels ...................................... 5 1.3.1 TheNavier-Stokesequation......................... 5 1.3.2 Thebasicidea.................................... 7 1.3.3 Top-downversusbottom-up........................ 9 1.3.4 LGCAversusmoleculardynamics................... 9 2 Cellular Automata ......................................... 13 2.1 What are cellular automata? . 13 2.2 A short history of cellular automata . 14 2.3 One-dimensional cellular automata . 15 2.3.1 Qualitative characterization of one-dimensional cellular automata . 22 2.4 Two-dimensional cellular automata . 28 2.4.1 Neighborhoodsin2D.............................. 28 2.4.2 Fredkin’s game . 29 2.4.3 ‘Life’ ............................................ 30 2.4.4 CA: what else? Further reading . 34 2.4.5 FromCAtoLGCA................................ 35 VI Contents 3 Lattice-gas cellular automata .............................. 37 3.1 The HPP lattice-gas cellular automata . 37 3.1.1 Modeldescription................................. 37 3.1.2 Implementation of the HPP model: How to code lattice-gas cellular automata? . 42 3.1.3 Initialization...................................... 46 3.1.4 Coarse graining . 48 3.2 The FHP lattice-gas cellular automata . 51 3.2.1 The lattice and the collision rules . 51 3.2.2 MicrodynamicsoftheFHPmodel .................. 57 3.2.3 The Liouville equation . 62 3.2.4 Massandmomentumdensity......................