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The Greenberg–Hastings Cellular Automaton (abbrev. GH model) is a three state two dimensional cellular automaton (abbrev CA) named after James M. Greenberg and Stuart Hastings, designed to model excitable media, One advantage of a CA model is ease of computation. The model can be understood quite well using simple "hand" calculations, not involving a computer.〔 Another advantage is that, at least in this case, one can prove a theorem characterizing those initial conditions which lead to repetitive behavior. ==Informal description== As in a typical two dimensional cellular automaton,〔 consider a rectangular grid, or checkerboard pattern, of "cells". It can be finite or infinite in extent. Each cell has a set of "neighbors". In the simplest case, each cell has four neighbors, those being the cells directly above or below or to the left or right of the given cell.〔 Like this: the b's are all of the neighbors of the a. The a is one of the neighbors of each of the b's. b b a b b At each "time" t=0,1,2,3,...., each cell is assigned one of three "states", typically called "resting" (or "quiescent" ; see excitable medium), "excited", or "refractory".〔 The assignment of states for all cells is arbitrary for t = 0, and then at subsequent times the state of each cell is determined by the following rules.〔 1. If a cell is in the excited state at time t then it is in the refractory state at time t+1. 2. If a cell is in the refractory state at time t then it is in the resting state at time t+1. 3. If a given cell is in the resting state at time t, and at least one of its neighbors is in the excited state at time t, then the given cell is in the excited state at time t+1. If a cell is in the resting state at time t and no neighbor is excited at time t, then the given cell is still in the resting state at time t+1. In this way the whole grid of cells advances from their initial states at t = 0 to their states at t = 1, then to their states at t = 2,3,4, etc., producing a pattern of cells in the various states for each time. See the first animation in Belousov-Zhabotinsky reaction for a striking example of behavior that can be exhibited by this model. The three states are indicated by different colors. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Greenberg–Hastings cellular automaton」の詳細全文を読む スポンサード リンク
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