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I don't understand how the border topologies change the game of life compared to when it's set on a regular plane You say it can be played on a variety of mani
by sebstefan 4y ago
I don't understand how the border topologies change the game of life compared to when it's set on a regular plane
You say it can be played on a variety of manifolds, but if the topology of a manifold "locally resembles Euclidean space near each point", considering that the game of life rules are always super local, then how does that change anything compared to a plane
- pfortuny 4y agoThere are interactions which are impossible in the square but are real in a torus or cylinder. For instance, periodic patterns may appear due to translations which do not in the square.
- autopilot23 4y agoYou can see the change only at the boundaries of the grid. Away from the boundary it is just like regular game of life but at the boundaries the definition of 'neighbour cell' changes based on the way the grid is glued (i.e its topology)
- Someone 4y agoFor the torus, what you call the boundary is no different from any of the other cells. If you were to live on such a grid, you’d be able to find out that it’s a torus and how many grid items there are, but you wouldn’t be able to see any difference between the individual grid cells.
- Someone 4y agoEarth is flat locally, too, but if you travel along a line for 40,000 km, you return to your starting point. That doesn’t happen on a plane. For this, the difference similarly only shows up over longer distances. That means more iterations. Spaceships will return where they left off. Also, the specific topology matters: if a spaceship makes a tour around the world, it may appear to have flipped over on a Klein bottle.