Life[M List?Matrixq, {G1 Integer?Nonnegative, G2 Integer?Nonnegative}] := Cellularautomaton[ { 224, {2, {{2, 2, 2}, {2, 1, 2}, {
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50 Examples Documentation Release 1.0
50 Examples Documentation Release 1.0 A.M. Kuchling Apr 13, 2017 Contents 1 Introduction 3 2 Convert Fahrenheit to Celsius5 3 Background: Algorithms 9 4 Background: Measuring Complexity 13 5 Simulating The Monty Hall Problem 17 6 Background: Drawing Graphics 23 7 Simulating Planetary Orbits 29 8 Problem: Simulating the Game of Life 35 9 Reference Card: Turtle Graphics 43 10 Indices and tables 45 i ii 50 Examples Documentation, Release 1.0 Release 1.0 Date Apr 13, 2017 Contents: Contents 1 50 Examples Documentation, Release 1.0 2 Contents CHAPTER 1 Introduction Welcome to “50 Examples for Teaching Python”. My goal was to collect interesting short examples of Python programs, examples that tackle a real-world problem and exercise various features of the Python language. I envision this collection as being useful to teachers of Python who want novel examples that will interest their students, and possibly to teachers of mathematics or science who want to apply Python programming to make their subject more concrete and interactive. Readers may also enjoy dipping into the book to learn about a particular algorithm or technique, and can use the references to pursue further reading on topics that especially interest them. Python version All of the examples in the book were written using Python 3, and tested using Python 3.2.1. You can download a copy of Python 3 from <http://www.python.org/download/>; use the latest version available. This book is not a Python tutorial and doesn’t try to introduce features of the language, so readers should either be familiar with Python or have a tutorial available. -
Martin Gardner Papers SC0647
http://oac.cdlib.org/findaid/ark:/13030/kt6s20356s No online items Guide to the Martin Gardner Papers SC0647 Daniel Hartwig & Jenny Johnson Department of Special Collections and University Archives October 2008 Green Library 557 Escondido Mall Stanford 94305-6064 [email protected] URL: http://library.stanford.edu/spc Note This encoded finding aid is compliant with Stanford EAD Best Practice Guidelines, Version 1.0. Guide to the Martin Gardner SC064712473 1 Papers SC0647 Language of Material: English Contributing Institution: Department of Special Collections and University Archives Title: Martin Gardner papers Creator: Gardner, Martin Identifier/Call Number: SC0647 Identifier/Call Number: 12473 Physical Description: 63.5 Linear Feet Date (inclusive): 1957-1997 Abstract: These papers pertain to his interest in mathematics and consist of files relating to his SCIENTIFIC AMERICAN mathematical games column (1957-1986) and subject files on recreational mathematics. Papers include correspondence, notes, clippings, and articles, with some examples of puzzle toys. Correspondents include Dmitri A. Borgmann, John H. Conway, H. S. M Coxeter, Persi Diaconis, Solomon W Golomb, Richard K.Guy, David A. Klarner, Donald Ervin Knuth, Harry Lindgren, Doris Schattschneider, Jerry Slocum, Charles W.Trigg, Stanislaw M. Ulam, and Samuel Yates. Immediate Source of Acquisition note Gift of Martin Gardner, 2002. Information about Access This collection is open for research. Ownership & Copyright All requests to reproduce, publish, quote from, or otherwise use collection materials must be submitted in writing to the Head of Special Collections and University Archives, Stanford University Libraries, Stanford, California 94304-6064. Consent is given on behalf of Special Collections as the owner of the physical items and is not intended to include or imply permission from the copyright owner. -
The Game of Life Trad
The Game of Life -“If I sometimes smoked one way [...] sometimes another, sometimes not at all, varied the way I dressed, was nervous, serene, ambitious, lazy, lecherous, gluttonous, ascetic – where would my `self ́ be? What would I achieve? It’s the way a man chooses to limit himself that determines his character. A man without habits, consistency, redundancy – and hence boredom – is not human. He’s insane.” -“And accepting these self- defeating limitations is mental health?” I said. Luke Rhinehart, The Dice Man, Harper-Collins, 1999, pp. 65-66. Gaël Charbau: A “retrospective”... there’s a word I never thought I’d use about your work at such an early stage. Maybe “introspective” is a better description of this short exploration of your work. The larousse dictionary defines “introspection” as: “methodical observation of personal states of consciousness and inner life.” What are your thoughts? Gilles Barbier: Some of the work is twenty-five years old. That’s half my life. The direction of my work, however, has been based on drift and retrospective narratives have difficulty mapping out this fluid form which has no backbone. It isn’t easy to recount twenty-five years of drifting on an artificial lake without currents, winds, wrecks and islands, without making what is a maiden voyage appear disordered and agitated. This is my relationship to art. It is easier to talk about the holes, the bananas, the leaks, the insatiable hunger, the engines cutting out, the desire for treasure, and the great absentee, time, which is manifest only through its effects. GC: I wanted to ask you about the holes theme. -
Tony Smith Complex Systems Analyst Meme Media [email protected]
Golly: how an open source project took over the study of cellular automata. Tony Smith Complex Systems Analyst Meme Media [email protected] Open Source Developers' Conference Thursday, 25 November 2010, 14:30 Melbourne, Australia 1 A long prehistory The basic idea: A grid of cells in which the next state of each cell is determined by the previous state of the cells in its immediate neighbourhood through some rule. John Horton Conway discovered an interesting rule whereby a live cell would stay live if it had two or three live neighbours of eight and an empty cell would turn live if it had exactly three, calling it the Game of Life and having it described in Martin Gardner’s Mathematical Games column in Scientific American in October 1970. In the article Conway offered a $50 prize to the first person who, before the end of 1970, could prove or disprove his initial conjecture that no pattern can grow indefinitely. One way to disprove it would be to discover patterns that keep adding counters to the field: a gun, which would be a configuration that repeatedly shoots out moving objects such as the glider. The prize was won that November by a team from the Massachusetts Institute of Technology, led by Bill Gosper. 2 Cellular Automata needed computers • Ed Fredkin’s trivial solution to reproducing patterns in cellular automata reported in Scientific American in 1983. • Wolfram, Stephen, “Universality and Complexity in Cellular Automata,” Physica D, 1984, 10 (January) 1-35. Classes 1-4. • Poundstone, William, The Recursive Universe: Cosmic Complexity and the Limits of Scientific Knowledge, Chicago: Contemporary Books, 1985. -
Conway's Game of Life Accelerated with Opencl
Conway's Game of Life accelerated with OpenCL Thomas Rumpf Friedrich-Schiller-University Jena, Germany Department of Mathematics and Computer Science [email protected] Abstract. We introduce a massively data-parallel implementation of John Conway's cellular automaton Game of Life in-silico which provides the user with a high flexibility to modify initial settings and progression rules. Written in C/C++ and employing the open programming inter- face OpenCL our program utilizes the parallel computing architecture of modern graphics cards leading to a significant speed-up in estimat- ing artificial life-form generations in comparison to ordinary CPU-based implementations. Custom input files for specification of initial configu- rations as well as a variety of features to control the course of the game on the fly contribute to improve the productivity in conducting experi- mental studies using our cellular automaton framework. Key words: Game of Life, OpenCL, OpenGL, parallel computing, GPGPU 1 Introduction John Conway designed the cellular automaton Game of Life in 1970 to prove that it is possible to build a simple yet powerful machine which can simulate the basic concepts of life. The outcome of his automaton had to be unpredictable meeting three desiderata: firstly there should be no initial pattern for which there is a simple proof that the population can grow without limit, secondly initial patterns that apparently do grow without limit and thirdly initial patterns fading away, settling into a stable configuration or entering an oscillating phase [2]. He achieved these goals employing a simple two-dimensional board of equally shaped cells which had only two states { dead or alive. -
Life Algorithms
Life Algorithms Tomas Rokicki June 28, 2018 Abstract We describe some ideas on how to implement Conway’s Game of Life. 1 Introduction Conway’s Game of Life serves as the “Hello World” of recreational computing. Many of us who cut our teeth on minicomputers or microcomputers will remember writing our own implementations, and then struggling to make them faster [5]. In this paper we briefly describe some of the more interesting ways to implement Life, without taking the fun out of getting all the details of implementation exactly correct. We will focus on calculating subsequent generations from current generations, ignoring the impact on other operations such as loading and saving patterns, setting and clearing cells, calculating the current population of the universe, and displaying the pattern. We will also ignore the impact of the borders (if any) of the universe. In a real Life program, all of these are important aspects that should be considered before adopting a too-complex algorithm. All the code for this paper is available at https://github.com/rokicki/lifealg along with more in- formation and performance comparisons. We include the algorithms in the Golly program as well as high-performance algorithms created by Adam Goucher as part of his lifelib project. 2 Elementary Approaches: Arrays 2.1 Basic Algorithm The most fundamental implementation of the Game of Life uses two two-dimensional arrays repre- senting the current universe and the universe in the next generation. Computing the next generation array from the current generation array involves iterating over all the cell positions, calculating the number of live neighbors to that cell from the current generation array, and then determining if the next generation cell is alive or dead based on this neighbor count and the life status of the current generation cell. -
Large Scale Cellular Automata on Fpgas: a New Generic Architecture and a Framework
Large Scale Cellular Automata on FPGAs: A New Generic Architecture and a Framework NIKOLAOS KYPARISSAS∗ and APOSTOLOS DOLLAS, Technical University of Crete, Greece Cellular Automata (CA) are discrete mathematical models discovered in the 1940s by John von Neumann and Stanislaw Ulam, and used extensively in many scientific disciplines ever since. The present work evolved from a Field Programmable Gate Array (FPGA)-based design to simulate urban growth into a generic architecture which is automatically generated by a framework to efficiently compute complex cellular automata with large 29 × 29 neighborhoods in Cartesian or toroidal grids, with 16- or 256-states per cell. The new architecture and the framework are presented in detail, including results in terms of modeling capabilities and performance. Large neighborhoods greatly enhance CA modeling capabilities, such as the implementation of anisotropic rules. Performance-wise, the proposed architecture runs on a medium-size FPGA up to 51 times faster vs. a CPU running highly optimized C code. Compared to GPUs the speedup is harder to quantify because CA results have been reported on GPU implementations with neighborhoods up to 11 × 11, in which case FPGA performance is roughly on par with GPU; however, based on published GPU trends, for 29 × 29 neighborhoods the proposed architecture is expected to have better performance vs. a GPU, at one-tenth the energy requirements. The architecture and sample designs are open source available under the creative commons license. CCS Concepts: • Computer systems organization ! Real-time system architecture; Special purpose systems; • Computing methodologies ! Real-time simulation; • Hardware ! Reconfigurable logic applications; Hardware accelerators. Additional Key Words and Phrases: cellular automata, generic architecture, framework, FPGA accelerator ACM Reference Format: Nikolaos Kyparissas and Apostolos Dollas. -
Solvers to Search for Patterns
Searching for patterns in Conway’s Game of Life Town Cape of Johan Bontes Minor dissertation presented in partial fulfilment of the requirements for the degree of Master of Science in the department of Computer Science UniversityUniversity of Cape Town Supervisor: Prof. James Gain 18 September 2019 The copyright of this thesis vests inTown the author. No quotation from it or information derived from it is to be published without full acknowledgement of the source. The thesis is to be used for private study or non- commercial research purposes Capeonly. of Published by the University of Cape Town (UCT) in terms of the non-exclusive license granted to UCT by the author. University 2 Abstract Conway’s Game of Life (Life) is a simple cellular automaton, discovered by John Conway in 1970, that exhibits complex emergent behavior. Life-enthusiasts have been looking for building blocks with specific properties (patterns) to answer unsolved problems in Life for the past five decades. Finding patterns in Life is difficult due to the large search space. Current search algorithms use an explorative approach based on the rules of the game, but this can only sample a small fraction of the search space. More recently, people have used Sat solvers to search for patterns. These solvers are not specifically tuned to this problem and thus waste a lot of time processing Life’s rules in an engine that does not understand them. We propose a novel Sat-based approach that replaces the binary tree used by traditional Sat solvers with a grid-based approach, complemented by an injection of Game of Life specific knowledge.