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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. -
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..................... -
The Fantastic Combinations of John Conway's New Solitaire Game "Life" - M
Mathematical Games - The fantastic combinations of John Conway's new solitaire game "life" - M. Gardner - 1970 Suche Home Einstellungen Anmelden Hilfe MATHEMATICAL GAMES The fantastic combinations of John Conway's new solitaire game "life" by Martin Gardner Scientific American 223 (October 1970): 120-123. Most of the work of John Horton Conway, a mathematician at Gonville and Caius College of the University of Cambridge, has been in pure mathematics. For instance, in 1967 he discovered a new group-- some call it "Conway's constellation"--that includes all but two of the then known sporadic groups. (They are called "sporadic" because they fail to fit any classification scheme.) Is is a breakthrough that has had exciting repercussions in both group theory and number theory. It ties in closely with an earlier discovery by John Conway of an extremely dense packing of unit spheres in a space of 24 dimensions where each sphere touches 196,560 others. As Conway has remarked, "There is a lot of room up there." In addition to such serious work Conway also enjoys recreational mathematics. Although he is highly productive in this field, he seldom publishes his discoveries. One exception was his paper on "Mrs. Perkin's Quilt," a dissection problem discussed in "Mathematical Games" for September, 1966. My topic for July, 1967, was sprouts, a topological pencil-and-paper game invented by Conway and M. S. Paterson. Conway has been mentioned here several other times. This month we consider Conway's latest brainchild, a fantastic solitaire pastime he calls "life". Because of its analogies with the rise, fall and alternations of a society of living organisms, it belongs to a growing class of what are called "simulation games"--games that resemble real-life processes. -
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. -
Life[M List?Matrixq, {G1 Integer?Nonnegative, G2 Integer?Nonnegative}] := Cellularautomaton[ { 224, {2, {{2, 2, 2}, {2, 1, 2}, {
Life The best-known two-dimensional cellular automaton, invented by John H. Conway and popularized in Martin Gardner's Scientific American column starting in October 1970. Life, sometimes also called "the game of life," was originally played (i.e., successive generations were produced) by hand with counters, but implementation on a computer greatly increased the ease of exploring patterns. The life cellular automaton is run by placing a number of filled cells on a two-dimensional grid. Each generation then switches cells on or off depending on the state of the cells that surround it. The rules are defined as follows. All eight of the cells surrounding the current one are checked to see if they are on or not. Any cells that are on are counted, and this count is then used to determine what will happen to the current cell. 1. Death: if the count is less than 2 or greater than 3, the current cell is switched off. 2. Survival: if (a) the count is exactly 2, or (b) the count is exactly 3 and the current cell is on, the current cell is left unchanged. 3. Birth: if the current cell is off and the count is exactly 3, the current cell is switched on. The game of life is a totalistic cellular automaton, and can be implemented as follows using the built-in command CellularAutomaton, where the initial conditions are specified as a binary matrix and the results for generations through are returned. (Here, corresponds to the initial pattern.) Life[m_List?MatrixQ, {g1_Integer?NonNegative, g2_Integer?NonNegative}] := CellularAutomaton[ { 224, {2, {{2, 2, 2}, {2, 1, 2}, {2, 2, 2}}}, {1, 1} }, {m, 0}, g2, { {g1, g2}, Automatic }] /; g2>=g1 Weisstein gives an extensive alphabetical tabulation of life forms and terms. -
Easychair Preprint a Game of Life on a Pythagorean Tessellation
EasyChair Preprint № 5345 A Game of Life on a Pythagorean Tessellation Soorya Annadurai EasyChair preprints are intended for rapid dissemination of research results and are integrated with the rest of EasyChair. April 18, 2021 A Game of Life on a Pythagorean Tessellation Soorya Annadurai Microsoft R&D Pvt. Ltd. Bangalore, India [email protected] Abstract—Conway’s Game of Life is a zero-player game played 3) Births. Each empty cell adjacent to exactly three neigh- on an infinite square grid, where each cell can be either ”dead” bors is a birth cell. It will become alive in the next or ”alive”. The interesting aspect of this game arises when we generation. observe how each cell interacts with its neighbors over time. There has been much public interest in this game, and several In a cellular automaton of this type, a single cell may do variants have become popular. Research has shown that similar one of four things within a single time step[6]: If it was dead Games of Life can exist on hexagonal, triangular, and other tiled but becomes alive, we say that it is born. If it was alive and grids. Games of Life have also been devised in 3 dimensions. remains alive, we say that it survives. If it was alive and In this work, another Game of Life is proposed that utilizes a Pythagorean tessellation, with a unique set of rules. Several becomes dead, we say that it dies. And if it was dead and interesting life forms in this universe are also illustrated. -
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. -
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. -
Ramifying Feedback Networks, Cross-Scale Interactions, And
Ramifying Feedback Networks, Nicholas M. Gotts* Cross-Scale Interactions, and Macaulay Land Use Research Institute Emergent Quasi Individuals in Conway’s Game of Life Keywords Feedback network, cross-scale interaction, cellular automata, emergence Abstract Small patterns of state 1 cells on an infinite, otherwise empty array of Conway’s game of Life can produce sets of growing structures resembling in significant ways a population of spatially situated individuals in a nonuniform, highly structured environment. Ramifying feedback networks and cross-scale interactions play a central role in the emergence and subsequent dynamics of the quasi population. The implications are discussed: It is proposed that analogous networks and interactions may have been precursors to natural selection in the real world. 1 Introduction There are small patterns of state 1 cells on an infinite, otherwise empty array of Conway’s game of Life [5], which manifest a long-sustained increase in structural and dynamic complexity, and produce sets of growing structures resembling in significant ways a group of spatially situated individual organisms interacting with a nonuniform environment. These quasi individuals’ interaction with the environment and each other, but not their internal makeup, appears lifelike: They grow (although having no metab- olism), affect their neighbors’ survival, and influence the appearance of new group members (although no genetic mechanism is involved). Ramifying (self-extending) feedback networks and cross-scale in- teractions are central to the emergence and subsequent dynamics of these quasi individuals. Conway’s game of Life (henceforth GoL) is a synchronous, deterministic, binary cellular automaton (CA), run on a two-dimensional array of rectangular cells (infinite, or finite and toroidal). -
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. -
Symbiosis Promotes Fitness Improvements in the Game of Life
Symbiosis Promotes Fitness Improvements in the Game of Life Peter D. Turney* Submitted to: Artificial Life. Category: Article. Date: June 15, 2020. 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 Conway’s 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. Keywords: Symbiosis, cooperation, open-ended evolution, Game of Life, Immigration Game, levels of selection. * Ronin Institute, 127 Haddon Place, Montclair, NJ 07043-2314, USA, [email protected], 819-661-4625. P. D. Turney Symbiosis Promotes Fitness Improvements 1 Introduction There are two main definitions of symbiosis in biology, (1) symbiosis as any association and (2) symbiosis as persistent mutualism [7]. -
Programmare Un Sintetizzatore Con Automi Cellulari
Alma Mater Studiorum UniversitadiBologna` · FACOLTA` DI SCIENZE MATEMATICHE, FISICHE E NATURALI Corso di Laurea in Scienze di Internet Programmare un sintetizzatore con Automi Cellulari Tesi di Laurea in Programmazione Internet Relatore: Presentata da: Chiar.mo Prof. Armando Viliam Fortunato Antonio Messina Sessione III Anno Accademico 2010/2011 Indice (1) Introduzione ...........................................................................................5 1.1 Precedenti ..................................................................................6 (2) Automi Cellulari 2.1 Cosa sono? ................................................................................11 2.2 Come funzionano? .....................................................................13 2.3 Sistemi Dinamici e classi di Automi Cellulari ..............................17 2.4 Computazione Universale e Automi Cellulari ..............................21 2.5 Game of Life ...............................................................................23 - Come funziona .....................................................................23 - Pattern di Stati ....................................................................24 - Oggetti statici e oggetti ripetitivi .........................................25 2.6 Spacefiller e Breeder ...................................................................29 2.7 Supercolliders .............................................................................31 2.8 Auto-riproducibilità ...................................................................33