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Not much to the article, so I guess the interesting part is the actual game: https://scratch.mit.edu/projects/164407978/#fullscreen https://scratch.mit.edu/proj

Not much to the article, so I guess the interesting part is the actual game: https://scratch.mit.edu/projects/164407978/#fullscreen https://scratch.mit.edu/projects/164407978/#fullscreen > It’s a slightly unusual implementation in that the surface of the game is, in effect, spherical – i.e. the edges are effectively a feature of the projection of the surface but left joins to right, top to bottom and so on. I believe that is a torus, and not at all an unusual implementation choice for the Game of Life.

robobro 9y ago
Correct -- it's simple and satisfying, and arguably a more interesting 3D projection
Retr0spectrum 9y ago
I wrote an implementation a while back which actually projects it onto a 3d torus. I can't find the code now, but it looked something like this: https://i.ytimg.com/vi/lxIeaotWIks/hqdefault.jpg https://i.ytimg.com/vi/lxIeaotWIks/hqdefault.jpg but with a trefoil knot for extra flair.
kmill 9y ago
Yeah, I was wondering how they pulled a sphere off! (So I suspected it was just a flat torus instead -- for non-geometers, a flat torus is what the game Asteroids is played on. Unlike the usual embedding of a torus in 3D, the curvature of a flat torus is 0 everywhere.) I think the only possible convex sphere made of squares is six nxn square grids stuck together into a big cube. Supposing n>=2, then there are 24 squares with the defect that they only have 7 neighbors. Flat tori don't have any defects, so game of life creatures can't locally measure they're not just in two-dimensional Euclidean space. A wilder topology I've never seen the game of life take place on is 2d real projective space. Instead of just gluing bottom to top, side to side, you reverse the orientation as you glue. So, if your Asteroids spaceship is flying upward near the left side of the screen, when it goes past the top edge it would appear at the bottom edge flying upward near the right side of the screen. You could also play on a Klein bottle by reversing only one of the orientations.

robobro 9y ago

Correct -- it's simple and satisfying, and arguably a more interesting 3D projection

Retr0spectrum 9y ago

I wrote an implementation a while back which actually projects it onto a 3d torus. I can't find the code now, but it looked something like this: https://i.ytimg.com/vi/lxIeaotWIks/hqdefault.jpg https://i.ytimg.com/vi/lxIeaotWIks/hqdefault.jpg but with a trefoil knot for extra flair.

kmill 9y ago

Yeah, I was wondering how they pulled a sphere off! (So I suspected it was just a flat torus instead -- for non-geometers, a flat torus is what the game Asteroids is played on. Unlike the usual embedding of a torus in 3D, the curvature of a flat torus is 0 everywhere.) I think the only possible convex sphere made of squares is six nxn square grids stuck together into a big cube. Supposing n>=2, then there are 24 squares with the defect that they only have 7 neighbors. Flat tori don't have any defects, so game of life creatures can't locally measure they're not just in two-dimensional Euclidean space. A wilder topology I've never seen the game of life take place on is 2d real projective space. Instead of just gluing bottom to top, side to side, you reverse the orientation as you glue. So, if your Asteroids spaceship is flying upward near the left side of the screen, when it goes past the top edge it would appear at the bottom edge flying upward near the right side of the screen. You could also play on a Klein bottle by reversing only one of the orientations.