Cellular Automata - Maple Programming Help

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Cellular Automata

Main Concept

A cellular automaton is a collection of cells on a grid, each of which is born, lives, or dies at discrete time steps according to the population density of its neighbors at the previous time step. A popular version for cellular automata is Conway's Game of Life, which is defined by the following iteration rules:



A neighbor is any cell directly adjacent (North, South, East, West) or diagonally adjacent (NW, NE, SE, SW) to a given grid location.


A cell is born in an empty grid location at time k+1 if that location has exactly 3 neighbor cells at time k. Otherwise that grid location remains empty.


A cell survives at time k+1 if it has 2 or 3 neighbor cells at time k. Otherwise it dies.


Different instances of the game are distinguished by their initial conditions.


Many versions of cellular automata have interesting, semi-chaotic behaviors, and some can even be used for computation. For instance, Conway's Game of Life is known to be Turing complete, which means that in principle if the game were played on an infinite grid with no time constraints it could simulate any computer program.


Try this randomized grid demonstration, or even design your own rules. Toggle the check boxes to change the rules for the game. Change the density slider to alter the number of live starting cells. Click or drag on the box to draw cells while the simulation is paused. Use the Play, Pause, Next Step, and Reset buttons to control the simulation.


Cell is born when # of neighbors is:

Cell survives when # of neighbors is:


Cell Density


Grid Size




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