1 / 7

Cellular Automata

Cellular Automata. The Game The Game of Life is not your typical computer game. It is a 'cellular automation', and was invented by the Cambridge mathematician John Conway.

melody
Télécharger la présentation

Cellular Automata

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Cellular Automata

  2. The Game The Game of Life is not your typical computer game. It is a 'cellular automation', and was invented by the Cambridge mathematician John Conway. This game became widely known when it was mentioned in an article published by Scientific American in 1970. It consists of a collection of cells which, based on a few mathematical rules, can live, die or multiply. Depending on the initial conditions, the cells form various patterns throughout the course of the game.

  3. Cellular Automation Formally, we must think of an infinite square grid in which each cell exists in one or two states, „living“ or „dead“. Each cell is a simple automation that at every tick of a great clock must decide which state it will be in until the next tick. It makes this decision on the basis of not only its present state but also those of its eight neighbours, four adjacent along sides and four adjacent at corners.

  4. The Rules For a space that is 'populated': Each cell with one or no neighbours dies, as if by loneliness. Each cell with four or more neighbours dies, as if by overpopulation. Each cell with two or three neighbours survives. For a space that is 'empty' or 'unpopulated' Each cell with three neighbours becomes populated.

  5. The algorithm below computes successive generations for Life in matrix L. A 1 represents a live cell in the i,jth entry, and a 0 represents a dead cell. 1. for i  1 to 100 1. for j  1 to 100 1. s  0 2. for p i -1 to i +1 /compute effect for q  j - 1 to j +1 /of neighbours s  s + L(p,q) 3. s  s - L(i,j) 4. if (s = 3) or (s + L(i,j) = 3) then X(i,j) = 1 /store life or death else X(i,j) = 0 /in auxiliary array X 2. for i  1 to 100 1. for j  1 to 100 1. L(i,j)  X(i,j) /refresh L 2. display L(i,j) /display L

  6. The Game of Life A java applet: A dos program:

  7. Interesting links: www.bitstorm.org/gameoflife www.math.com/students/wonders/life/lif.html hensel.lifepatterns.net http://wwwhomes.uni-bielefeld.de/achim/gol.html

More Related