cellular automata a presentation by csc. outline history one dimension ca two dimension ca...
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CELLULAR AUTOMATA
A Presentation By CSC
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OUTLINE
HistoryOne Dimension CATwo Dimension CATotalistic CA & Conway’s Game of LifeClassification of CA
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HISTORY
First CA: Ulam & von Neumann, 1940Simulation of crystal growthStudy of Self-replicating systems
What is CA?Mathematical idealizations of natural systemsConsist of a lattice of discrete identical sites,
each site taking on a finite set of, say, integer values.
The values evolve in discrete times, according to some rules depend on the state of neighboring sites
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ONE-DIMENSION CA
Binary, nearest-neighbor, one-dimensional256 rules, using Wolfram code
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ONE-DIMENSION CA
Rule 30:Chaotic, random number generator in
MathematicaBlack cells b(n), closely fit by the line b(n)
= nRule 110:
Class IV behavior, Turing-complete
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TWO DIMENSION CA
Neighborhood definition:von Neumann Neighborhood Moore Neighborhood
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TOTALISTIC CA
The state of each cell in a totalistic CA is represented by a number
The value of a cell at time t depends only on the sum of the values of the cells in its neighborhood
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CONWAY’S GAME OF LIFE
Invented by J.H.Conway, 1970. Became famous since an article in Scientific American 223, by Martin Gardner.
States of each cell are {0,1} Survive if neighbor’s sum is 2 or 3
Birth if sum is 3
Representation: S23/B3 or 23/3
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CONWAY’S GAME OF LIFE
Still Life, Ex: boat
Oscillator, Ex: Blinker
Spaceship Ex: Glider
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CONWAY’S GAME OF LIFE
Three phase oscillator
Guns, Ex:Glider Gun
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CLASSIFICATION OF CA
Class 1 : evolves to a homogeneous state. Class 2 : evolves to simple separated
periodic structures. Class 3 yields chaotic aperiodic patterns. Class 4 yields complex patterns of localized
structures, including propagating structures. (Wolfram, 1984)
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CLASSIFICATION OF CA
λ = number of neighborhood states that map to a non-quiescent state/total number of neighborhood states. (Langton, 1986)
Class 1: λ < 0.2
Class 2,4: 0.2 < λ < 0.4 Game of Life: 0.2734
Class 3: 0.4 < λ < 1