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Comment by bee_rider | Hacker News Reader

Game of life on a sphere could be nice. I never really liked how the gliders would just go off into nowhere.

Although I guess if we play with this too much there is a risk of inventing something like… Bloch's Game of Life or something.

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probably torus. could you actually discretize the sphere properly? isnt this like tessellating a soccer ball?

You can get the topology of a sphere with holes at the poles by wrapping left/right but not up/down, like the Civilization games. Or you can do it with no holes by having left/right wrap, and top/bottom do a different wrap where you come back from the same direction but halfway around horizontally. (Imagine the path crossing over the poles projected onto a Mercator map.)

> You can get the topology of a sphere with holes at the poles by wrapping left/right but not up/down, like the Civilization games.

That is just a cylinder.

The Game of Life implementation in this post is based on a torus. Watch the gliders when they go off the edge of the screen: they return from the other side!

Actually most of CA simulations are done on torus which is referred to as periodic boundary conditions in the literature. Alternatively you can also have null (or fixed) boundaries or reflective ones. If the initial configuration has compact support (finite number of non-null states) and the CA keeps null-neighborhoods as null in the next step, you can simulate infinite grids… but not many people bother to do it. Many many papers use finite grids on torus.

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