This is Conway's Game of Life in Minecraft.

Conway's Game of Life is a turn-based game that consists of a grid of cells. Each cell is either alive or dead. Each turn every cell checks the amount of alive neighbours.

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Rules:

If a living cell has 2 or 3 alive neighbours, it survives, otherwise it dies. If a dead cell has 3 neighbours, it is revived, otherwise it stays dead. This can lead to interesting and satisfying results.

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Commands:

To play the game, place an item frame on the white concrete on the ground. This will turn it alive.
Once you set up your layout, you can start the simulation by typing "/function gameoflife:start".
To stop it, type "/function gameoflife:stop".
To clear the world of alive cells, type "/function gameoflife:clear".
If you want to progress just a single turn, type "/function gameoflife:step".

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There are a lot of unique patterns, so if you're interested, the link below will show you some examples, but to get the most out of it you should really just play around with it and see what happens.

bitstorm.org/gameoflife/lexicon/