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Conway's Game of Life
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==Rules== The universe of the Game of Life is [[Square tiling|an infinite, two-dimensional orthogonal grid of square]] ''cells'', each of which is in one of two possible states, ''live'' or ''dead'' (or ''populated'' and ''unpopulated'', respectively). Every cell interacts with its eight ''[[Moore neighborhood|neighbours]]'', which are the cells that are horizontally, vertically, or diagonally adjacent. At each step in time, the following transitions occur: # Any live cell with fewer than two live neighbours dies, as if by underpopulation. # Any live cell with two or three live neighbours lives on to the next generation. # Any live cell with more than three live neighbours dies, as if by overpopulation. # Any dead cell with exactly three live neighbours becomes a live cell, as if by reproduction. The initial pattern constitutes the ''seed'' of the system. The first generation is created by applying the above rules simultaneously to every cell in the seed, live or dead; births and deaths occur simultaneously, and the discrete moment at which this happens is sometimes called a ''tick''.{{#tag:ref|The simultaneity means that when each cell counts the number of live neighbours around it, it uses its neighbours' old states before the update, not their new states after the update. If the cells are instead updated in reading order, so that each cell uses the old states of the cells to its right and below it but the new states of the cells to its left and above it, a different cellular automaton results, which is known as NaiveLife<ref>{{cite web|title=NaiveLife Emulated: A reading-order simulation of Life|url=https://conwaylife.com/forums/viewtopic.php?f=11&t=4523&p=128919|website=ConwayLife.com|access-date=29 November 2021|language=en|date=24 May 2020}}</ref><ref>{{cite web|last1=Goucher|first1=Adam|title=Re: Thread For Your Accidental Discoveries|url=https://conwaylife.com/forums/viewtopic.php?f=2&t=279&p=13168#p13168|website=ConwayLife.com|access-date=29 November 2021|language=en|archive-date=29 November 2021|archive-url=https://web.archive.org/web/20211129154301/https://www.conwaylife.com/forums/viewtopic.php?f=2&t=279&p=13168#p13168|url-status=live}}</ref> because it is a common beginners' mistake among people attempting to program Conway's Game of Life.<ref>{{cite web|author1=Ian07|title=Re: Strange spaceship that is supposed to be impossible and infinite cell spread|url=https://conwaylife.com/forums/viewtopic.php?f=9&t=4288&p=88701#p88701|website=ConwayLife.com|access-date=29 November 2021|language=en|quote=I'm pretty sure this is because you've accidentally created an implementation of what's sometimes known as NaiveLife (as it's a common mistake made by many people coding CGoL for the first time):}}</ref>|group="nb"}} Each generation is a ''[[pure function]]'' of the preceding one. The rules continue to be applied repeatedly to create further generations. {{Conway's Game of Life gadget | autoplay = false | width = 400 | height = 300 | zoom = 8 | grid = on | cells = 0,0; 0,1; 0,-1; -1,0; 1,1 }}
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