Conway's Game of Life

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pages: 247 words: 43,430

Think Complexity by Allen B. Downey


Benoit Mandelbrot, cellular automata, Conway's Game of Life, Craig Reynolds: boids flock, discrete time,, Frank Gehry, Gini coefficient, Guggenheim Bilbao, mandelbrot fractal, Occupy movement, Paul Erdős, peer-to-peer, Pierre-Simon Laplace, sorting algorithm, stochastic process, strong AI, Thomas Kuhn: the structure of scientific revolutions, Turing complete, Turing machine, Vilfredo Pareto, We are the 99%

harmonics, Spectral Density hash function, Hashtables HashMap, Hashtables hashtables, Hashtables Hertz, Spectral Density Hist, Zipf’s Law histograms, Cumulative Distributions hoisting, Spectral Density holism, A New Kind of Model holistic model, Reductionism and Holism, Reductionism and Holism Homo economicus, The Axes of Scientific Models homogeneous, The Axes of Scientific Models hop, Stanley Milgram hurricane, Realism, Instrumentalism I id, Instrumentalism immutable objects, Representing Graphs implementing cellular automata, Implementing CAs implementing Game of Life, Implementing Life in operator, Analysis of Search Algorithms incompleteness, A New Kind of Thinking Incompleteness Theorem, A New Kind of Thinking indeterminism, A New Kind of Thinking indexing, Analysis of Basic Python Operations, Fast Fourier Transform infinite loop, Generators infinite sequence, Iterators inheritance, Representing Graphs, Representing Graphs __init__, Representing Graphs instantiate, CADrawer instrumentalism, A New Kind of Model, Instrumentalism interactions, minimizing, A New Kind of Engineering interface, CADrawer, CADrawer implementing, CADrawer specifying, CADrawer IPython, Summing Lists isolation of components, A New Kind of Engineering __iter__, Iterators iterator, Iterators iteritems, List Comprehensions itertools, Iterators J join, Analysis of Basic Python Operations K Kansas, Stanley Milgram kernel, Implementing Life KeyError, Hashtables Kosko, Bart, A New Kind of Thinking Kuhn, Thomas, Paradigm Shift?

Adding more detail, like features w and z, might make the model more realistic, but that realism adds no explanatory power. Figure 6-7. The logical structure of a simple physical model Chapter 7. Game of Life One of the first cellular automata to be studied (and probably the most popular of all time) is a 2D CA called “The Game of Life,” or GoL for short. It was developed by John H. Conway and popularized in 1970 in Martin Gardner’s column in Scientific American. See for more information. The cells in GoL are arranged in a 2D grid, either infinite in both directions or wrapped around. A grid wrapped in both directions is called a torus because it is topographically equivalent to the surface of a doughnut; see Each cell has two states (live and dead) and eight neighbors (north, south, east, west, and the four diagonals).

pages: 271 words: 52,814

pages: 489 words: 148,885

Accelerando by Stross, Charles


call centre, carbon-based life, cellular automata, cognitive dissonance, commoditize, Conway's Game of Life, dark matter, dumpster diving, Extropian, finite state, Flynn Effect, glass ceiling, gravity well, John von Neumann, knapsack problem, Kuiper Belt, Magellanic Cloud, mandelbrot fractal, market bubble, means of production, packet switching, performance metric, phenotype, planetary scale, Pluto: dwarf planet, reversible computing, Richard Stallman, SETI@home, Silicon Valley, Singularitarianism, slashdot, South China Sea, stem cell, technological singularity, telepresence, The Chicago School, theory of mind, Turing complete, Turing machine, Turing test, upwardly mobile, Vernor Vinge, Von Neumann architecture, web of trust, Y2K, zero-sum game

Each of these companies – and there are currently more than sixteen thousand of them, although the herd is growing day by day – has three directors and is the director of three other companies. Each of them executes a script in a functional language Manfred invented; the directors tell the company what to do, and the instructions include orders to pass instructions on to their children. In effect, they are a flock of cellular automata, like the cells in Conway's Game of Life, only far more complex and powerful. Manfred's companies form a programmable grid. Some of them are armed with capital in the form of patents Manfred filed, then delegated rather than passing on to one of the Free Foundations. Some of them are effectively nontrading, but occupy directorial roles. Their corporate functions (such as filing of accounts and voting in new directors) are all handled centrally through his company-operating framework, and their trading is carried out via several of the more popular B2B enabler dot-coms.

pages: 846 words: 232,630

Darwin's Dangerous Idea: Evolution and the Meanings of Life by Daniel C. Dennett


Albert Einstein, Alfred Russel Wallace, anthropic principle, assortative mating, buy low sell high, cellular automata, combinatorial explosion, complexity theory, computer age, conceptual framework, Conway's Game of Life, Danny Hillis, double helix, Douglas Hofstadter, Drosophila, finite state, Gödel, Escher, Bach, In Cold Blood by Truman Capote, invention of writing, Isaac Newton, Johann Wolfgang von Goethe, John von Neumann, Murray Gell-Mann, New Journalism, non-fiction novel, Peter Singer: altruism, phenotype, price mechanism, prisoner's dilemma, QWERTY keyboard, random walk, Richard Feynman, Richard Feynman, Rodney Brooks, Schrödinger's Cat, selection bias, Stephen Hawking, Steven Pinker, strong AI, the scientific method, theory of mind, Thomas Malthus, Turing machine, Turing test

So this seems at first to be a striking demonstration that natural selection cannot be the source of organization and order after all — which would indeed be the downfall of the Darwinian idea. But there is another way of looking at it, as we have seen. What conditions have to be in effect for evolution by natural selection to occur? The words 1 put into Darwin's mouth were simple: Give me Order, and time, and I will give you Design. But what we have subsequently learned is that not every variety of Order is sufficient for evolvability. As we saw illustrated by Conway's Game of Life, you have to have just the right sort of Order, with just the right mix of freedom and constraint, growth and decay, rigidity and fluidity, for good things to happen at all. You only get evolution, as the Santa Fe motto proclaims, on the edge of chaos, in the regions of possible law that {222} form the hybrid zone between stifling order and destructive chaos. Fortunately, our portion of the universe is poised in just such a zone, in which the conditions for evolvability are tuned just right.

pages: 329 words: 106,831

All Your Base Are Belong to Us: How Fifty Years of Video Games Conquered Pop Culture by Harold Goldberg


Alexey Pajitnov wrote Tetris, Apple II, cellular automata, Columbine, Conway's Game of Life, game design, In Cold Blood by Truman Capote, Mars Rover, Mikhail Gorbachev, Ralph Waldo Emerson, Ray Oldenburg, Saturday Night Live, Silicon Valley, Steve Jobs, Steve Wozniak, The Great Good Place, Thorstein Veblen, urban planning

As well, when Maxis was still a public company, Braun had shown Wright a 1985 Activision game for the Apple II called Little Computer People. Little Computer People was occasionally hilarious and featured a slow-moving cartoonlike character called Darren who would write you letters saying, “I have many hobbies that occupy my time.” To prove it, he watched TV, exercised, and searched for someone to live in his computer with him. Finally, Wright was impressed with John Horton Conway’s theories of cellular automata, which were espoused in The Game of Life. In his 1970s simulation game, Conway showed that you could emulate the complex patterns of the birth and death of organisms living together in society—and everything in between. All these combined to influence Wright as he dreamed up a project whose working title was Home Tactics, the Experimental Domestic Simulator. Wright later tweaked the name to the slightly more appealing Dollhouse.

pages: 448 words: 116,962

Singularity Sky by Stross, Charles


anthropic principle, cellular automata, Conway's Game of Life, cosmological constant, Doomsday Clock, Extropian, gravity well, Kuiper Belt, life extension, means of production, new economy, phenotype, prisoner's dilemma, skinny streets, technological singularity, uranium enrichment

Together they'd pieced together a terrifying hypothesis. "Herman was unusually vague about it," Martin admitted. "Normally he has a lot of background detail. Every word means something. But it's as if he doesn't want to say too much about the Festival. They're—he called them, uh, glider-gun factories. I don't know if you know about Life—" "Cellular automata, the game?" "That's the one. Glider guns are mobile cellular automata. There are some complex life structures that replicate themselves, or simpler cellular structures; a glider-gun factory is a weird one. It periodically packs itself into a very dense mobile system that migrates across the grid for a couple of hundred squares, then it unpacks itself into two copies that then pack down and fly off in opposite directions. Herman said that they're a real-space analogue: he called them a Boyce-Tipler robot.

pages: 410 words: 119,823

Radical Technologies: The Design of Everyday Life by Adam Greenfield

3D printing, Airbnb, augmented reality, autonomous vehicles, bank run, barriers to entry, basic income, bitcoin, blockchain, business intelligence, business process, call centre, cellular automata, centralized clearinghouse, centre right, Chuck Templeton: OpenTable, cloud computing, collective bargaining, combinatorial explosion, Computer Numeric Control, computer vision, Conway's Game of Life, cryptocurrency, David Graeber, dematerialisation, digital map, distributed ledger, drone strike, Elon Musk, ethereum blockchain, facts on the ground, fiat currency, global supply chain, global village, Google Glasses, IBM and the Holocaust, industrial robot, informal economy, information retrieval, Internet of things, James Watt: steam engine, Jane Jacobs, Jeff Bezos, job automation, John Conway, John Markoff, John Maynard Keynes: Economic Possibilities for our Grandchildren, John Maynard Keynes: technological unemployment, John von Neumann, joint-stock company, Kevin Kelly, Kickstarter, late capitalism, license plate recognition, lifelogging, M-Pesa, Mark Zuckerberg, means of production, megacity, megastructure, minimum viable product, money: store of value / unit of account / medium of exchange, natural language processing, Network effects, New Urbanism, Occupy movement, Oculus Rift, Pareto efficiency, pattern recognition, Pearl River Delta, performance metric, Peter Eisenman, Peter Thiel, planetary scale, Ponzi scheme, post scarcity, RAND corporation, recommendation engine, RFID, rolodex, Satoshi Nakamoto, self-driving car, sentiment analysis, shareholder value, sharing economy, Silicon Valley, smart cities, smart contracts, sorting algorithm, special economic zone, speech recognition, stakhanovite, statistical model, stem cell, technoutopianism, Tesla Model S, the built environment, The Death and Life of Great American Cities, The Future of Employment, transaction costs, Uber for X, universal basic income, urban planning, urban sprawl, Whole Earth Review, WikiLeaks, women in the workforce

pages: 1,201 words: 233,519

Coders at Work by Peter Seibel


Ada Lovelace, bioinformatics, cloud computing, Conway's Game of Life, domain-specific language, don't repeat yourself, Donald Knuth, fault tolerance, Fermat's Last Theorem, Firefox, George Gilder, glass ceiling, Guido van Rossum, HyperCard, information retrieval, Larry Wall, loose coupling, Marc Andreessen, Menlo Park, Metcalfe's law, Perl 6, premature optimization, publish or perish, random walk, revision control, Richard Stallman, rolodex, Ruby on Rails, Saturday Night Live, side project, slashdot, speech recognition, the scientific method, Therac-25, Turing complete, Turing machine, Turing test, type inference, Valgrind, web application

Seibel: You guys were building these computers from scratch in '76 to '79. Isn't that about the same time the Altair was coming out? Peyton Jones: That's right. Hobbyist computers were definitely starting to come out. But we considered those to be rather cheating. The thing about this machine that we built ourselves was that software was the problem. I think my most advanced program for this machine was Conway's Game of Life. That worked very nicely. But writing any kind of serious program, like a programming language, was just too much work because it had very limited permanent storage medium. And it was all typing in hexadecimal stuff—no assembler. Seibel: So more raw machine code. Peyton Jones: Of course the Cambridge mainframe understood BCPL so we were writing lots of BCPL programs. We were actually writing a compiler then for a programming language that we'd invented.

pages: 210 words: 62,771

pages: 405 words: 117,219

In Our Own Image: Savior or Destroyer? The History and Future of Artificial Intelligence by George Zarkadakis


3D printing, Ada Lovelace, agricultural Revolution, Airbnb, Alan Turing: On Computable Numbers, with an Application to the Entscheidungsproblem, anthropic principle, Asperger Syndrome, autonomous vehicles, barriers to entry, battle of ideas, Berlin Wall, bioinformatics, British Empire, business process, carbon-based life, cellular automata, Claude Shannon: information theory, combinatorial explosion, complexity theory, continuous integration, Conway's Game of Life, cosmological principle, dark matter, dematerialisation, double helix, Douglas Hofstadter, Edward Snowden, epigenetics, Flash crash, Google Glasses, Gödel, Escher, Bach, income inequality, index card, industrial robot, Internet of things, invention of agriculture, invention of the steam engine, invisible hand, Isaac Newton, Jacquard loom, Jacquard loom, Jacques de Vaucanson, James Watt: steam engine, job automation, John von Neumann, Joseph-Marie Jacquard, liberal capitalism, lifelogging, millennium bug, Moravec's paradox, natural language processing, Norbert Wiener, off grid, On the Economy of Machinery and Manufactures, packet switching, pattern recognition, Paul Erdős, post-industrial society, prediction markets, Ray Kurzweil, Rodney Brooks, Second Machine Age, self-driving car, Silicon Valley, speech recognition, stem cell, Stephen Hawking, Steven Pinker, strong AI, technological singularity, The Coming Technological Singularity, The Future of Employment, the scientific method, theory of mind, Turing complete, Turing machine, Turing test, Tyler Cowen: Great Stagnation, Vernor Vinge, Von Neumann architecture, Watson beat the top human players on Jeopardy!, Y2K

The journey of the individual parts towards forming a self-organised system appears then to be algorithmically determined: they are ‘attracted’ to self-organisation and, ultimately, to life. We do not yet know whether this attraction is governed by a general law for biology. However, we have discovered something that seems to point towards such a law: Rule 110, a recursive algorithm that is Turing complete and lifelike – and there might be more.23 This profound correlation between cellular automata and biological phenomena suggests that life is governed by recursive computations, probably similar – or identical – to cellular automata. There is one more special feature of complex computations that is worth noting. They are fractal-like and scale-invariant. This means that they repeat themselves at every scale. From microscopic organisms to weather systems and the formation of galactic clusters nature creates similar patterns of organisation and behaviour.

pages: 798 words: 240,182

The Transhumanist Reader by Max More, Natasha Vita-More


23andMe, Any sufficiently advanced technology is indistinguishable from magic, artificial general intelligence, augmented reality, Bill Joy: nanobots, bioinformatics, brain emulation, Buckminster Fuller, cellular automata, clean water, cloud computing, cognitive bias, cognitive dissonance, combinatorial explosion, conceptual framework, Conway's Game of Life, cosmological principle, data acquisition, discovery of DNA, Douglas Engelbart, Drosophila,, endogenous growth, experimental subject, Extropian, fault tolerance, Flynn Effect, Francis Fukuyama: the end of history, Frank Gehry, friendly AI, game design, germ theory of disease, hypertext link, impulse control, index fund, John von Neumann, joint-stock company, Kevin Kelly, Law of Accelerating Returns, life extension, lifelogging, Louis Pasteur, Menlo Park, meta analysis, meta-analysis, moral hazard, Network effects, Norbert Wiener, P = NP, pattern recognition, phenotype, positional goods, prediction markets, presumed consent, Ray Kurzweil, reversible computing, RFID, Richard Feynman, Ronald Reagan, silicon-based life, Singularitarianism, stem cell, stochastic process, superintelligent machines, supply-chain management, supply-chain management software, technological singularity, Ted Nelson, telepresence, telepresence robot, telerobotics, the built environment, The Coming Technological Singularity, the scientific method, The Wisdom of Crowds, transaction costs, Turing machine, Turing test, Upton Sinclair, Vernor Vinge, Von Neumann architecture, Whole Earth Review, women in the workforce, zero-sum game

The Singularity Is Near: When Humans Transcend Biology by Ray Kurzweil


additive manufacturing, AI winter, Alan Turing: On Computable Numbers, with an Application to the Entscheidungsproblem, Albert Einstein, anthropic principle, Any sufficiently advanced technology is indistinguishable from magic, artificial general intelligence, Asilomar, augmented reality, autonomous vehicles, Benoit Mandelbrot, Bill Joy: nanobots, bioinformatics, brain emulation, Brewster Kahle, Brownian motion, business intelligence,, call centre, carbon-based life, cellular automata, Claude Shannon: information theory, complexity theory, conceptual framework, Conway's Game of Life, cosmological constant, cosmological principle, cuban missile crisis, data acquisition, Dava Sobel, David Brooks, Dean Kamen, disintermediation, double helix, Douglas Hofstadter,, epigenetics, factory automation, friendly AI, George Gilder, Gödel, Escher, Bach, informal economy, information retrieval, invention of the telephone, invention of the telescope, invention of writing, Isaac Newton, iterative process, Jaron Lanier, Jeff Bezos, job automation, job satisfaction, John von Neumann, Kevin Kelly, Law of Accelerating Returns, life extension, lifelogging, linked data, Loebner Prize, Louis Pasteur, mandelbrot fractal, Mikhail Gorbachev, mouse model, Murray Gell-Mann, mutually assured destruction, natural language processing, Network effects, new economy, Norbert Wiener, oil shale / tar sands, optical character recognition, pattern recognition, phenotype, premature optimization, randomized controlled trial, Ray Kurzweil, remote working, reversible computing, Richard Feynman, Richard Feynman, Robert Metcalfe, Rodney Brooks, Search for Extraterrestrial Intelligence, selection bias, semantic web, Silicon Valley, Singularitarianism, speech recognition, statistical model, stem cell, Stephen Hawking, Stewart Brand, strong AI, superintelligent machines, technological singularity, Ted Kaczynski, telepresence, The Coming Technological Singularity, Thomas Bayes, transaction costs, Turing machine, Turing test, Vernor Vinge, Y2K, Yogi Berra