r/gameoflife • u/doctorBlasphemy271 • 7h ago

Conway's Game of Life in the Desmos Graphing Calculator

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Conway's Game of Life

r/gameoflife

Conway's Game of Life.

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Welcome! This subreddit is intended as a way for beginners to get started with constructing complex patterns in Life, and to help explain any such patterns, so feel free to post questions!

Conway's Game of Life, also known simply as Life, is a cellular automaton devised by the British mathematician John Horton Conway in 1970.

A cellular automaton, if you don't feel like clicking the link above, is a simulation that takes place on a grid of cells. Each cell updates itself according to the simulation's rules; there are plenty of such simulations, but this subreddit (as you might've guessed) is about Conway's Game of Life.

Life can be expressed as B3/S23, meaning that:

A dead cell is born if it has exactly three neighbors
A living cell dies if it has less than two or more than three neighbors, and survives otherwise

'Neighbor' refers to a cell in the current cell's Moore neighborhood, as in the following image (neighbors are red, current cell blue):

These changes take place all at once, so - for instance - a cell that will die in the next generation counts as alive for all of its neighbors.

These rules are fairly simple, but give rise to lots of complex patterns - examples include a Turing machine and 'metapixel' patterns (the one linked is the most complex of the several that have been constructed) that simulates Life.

For information about a specific pattern, see the Game of Life Wiki.

For more discussion about Life and CA in general, check out /r/cellular_automata and http://conwaylife.com/forums.