Just as spectacular as the concept of a Turing Machine being built in the Game of Life is the " 17c/45Ĭaterpillar spaceship"-a gigantic pattern involving over 10 million cells that travels across the universe. The details of this construction are available at Paul Rendell's site here. It is possible to build a pattern that acts like a finite state machine connected to two counters."Īlthough it may seem a bit convoluted, this idea became the basis for the construction of a Turing Machine within the Game of Life. It is possible to construct logic gates such as AND, OR and NOT using gliders. This "sliding block memory" can be used to simulate a counter. If three gliders are shot in just the right way, the block will move farther away. For example, if two gliders are shot at a block in just the right way, the block will move closer to the source of the gliders. "It is possible for gliders to interact with other objects in interesting ways. The Wikipedia article on the Game of Life notes: Wikipedia article on Conway's Game of Life
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Dennett has used the analog of Conway's Life "universe" extensively to illustrate the possible evolution of complex philosophical constructs, such as consciousness and free will, from the relatively simple set of deterministic physical laws governing our own universe." This optimization allows for real-time simulations with many more particles and therefore more complex and life-like structures. In 1992 John Conway raised a question about the patterns in his famous mathematical Game of Life: 'Is there a Godlike still-life, one that can only have existed for all time (apart from things that dont interfere with it)' Conway closed his note by adding 'Well, Im going out to get a hot dog now. The rules are as follows: Each cell lives in a square in a rectangular grid. For example, philosopher and cognitive scientist Daniel C. What is this This is an optimized version of Jeffrey Ventrella's 'Clusters', 'a particle microworld with ambiguous entities'. Conways Game of Life is a game invented by mathematician John Conway in 1970. The game can also serve as a didactic analogy, used to convey the somewhat counterintuitive notion that "design" and "organization" can spontaneously emerge in the absence of a designer. r/desmos - reddit Mandelbrot Orbits - Jeffrey Ventrella. It is interesting for physicists, biologists, economists, mathematicians, philosophers, generative scientists and others to observe the way that complex patterns can emerge from the implementation of very simple rules. Maps The Feigenbaum Map The Chaos Game The Mandelbrot Set Conways Game of Life Introduction. Life is an example of emergence and self-organization. "Ever since its publication, Conway's Game of Life has attracted much interest because of the surprising ways in which the patterns can evolve.
The emergence of complex behavior-sometimes chaotic and other times seemingly orderly-from the simple rules set out by the Game of Life has notable implications in many fields:
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