REDUCTIONISM is the most natural thing in the world to grasp. I first heard about Cook’s result in 1998 when he spoke at a workshop at the Santa Fe Institute.ĬHAPTER TWO Dynamics, Chaos, and PredictionĬHAPTER SEVEN Defining and Measuring ComplexityĬHAPTER EIGHT Self-Reproducing Computer ProgramsĬHAPTER TEN Cellular Automata, Life, and the UniverseĬHAPTER TWELVE Information Processing in Living SystemsĬHAPTER THIRTEEN How to Make Analogies (if You Are a Computer)ĬHAPTER FOURTEEN Prospects of Computer ModelingĬHAPTER SIXTEEN Applying Network Science to Real-World NetworksĬHAPTER NINETEEN The Past and Future of the Sciences of Complexity In the 1990s, Matthew Cook, one of Wolfram’s research assistants, finally proved that Rule 110 was indeed universal, and is perhaps the simplest known example of a universal computer. Since then several researchers have proved that simple cellular automata (such as the Game of Life) are universal. Turing’s proof that there exists a universal Turing machine was a triumph, as was von Neumann’s proof that his self-replicating automaton was also a universal computer. However, in general it is hard to prove that a particular cellular automaton, Turing machine, or any other device is universal. Įach cell has two states (live and dead) and eight neighbors (north, south, east, west, and the four diagonals).Īlan Turing: On Computable Numbers, with an Application to the Entscheidungsproblem,įrom Mathematics to the Technologies of Life and Death, A grid wrapped in both directions is called a torus because it is topographically equivalent to the surface of a doughnut see. The cells in GoL are arranged in a 2D grid, either infinite in both directions or wrapped around. See Conway_Game_of_Life for more information. Conway and popularized in 1970 in Martin Gardner’s column in Scientific American. 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. Join, Analysis of Basic Python Operations Isolation of components, A New Kind of Engineering Interactions, minimizing, A New Kind of Engineering Instrumentalism, A New Kind of Model, Instrumentalism Inheritance, Representing Graphs, Representing Graphs Indexing, Analysis of Basic Python Operations, Fast Fourier Transform Incompleteness Theorem, A New Kind of Thinking In operator, Analysis of Search Algorithms Implementing Game of Life, Implementing Life Implementing cellular automata, Implementing CAs Homogeneous, The Axes of Scientific Models Homo economicus, The Axes of Scientific Models Holistic model, Reductionism and Holism, Reductionism and Holism Thomas Kuhn: the structure of scientific revolutions,
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