ZenoRogue | Perpetuum mobile in Nil geometry @ZenoRogue | Uploaded May 2020 | Updated October 2024, 13 minutes ago.
Penrose staircases and triangles is Nil make us wonder whether we could make gravity point downwards and use it to make a perpetuum mobile.
Such gravity does not make much physical sense, but let's try anyway.
Instead of the native geodesic perspective projection that we have been using in most animations, here we use a Poincaré ball-like projection which maps geodesic spheres to spheres, followed by orthogonal projection to 2D.
In 0:00 the gravity points downwards, in 0:15 and 0:30 the projection is rotated by 30 degrees (and there are more balls).
I expected the effect we see here, because there are no horizontal surfaces in Nil with this gravity. See e.g. twitter.com/ZenoRogue/status/1187378654470430720 or youtu.be/HeFyuVs-Tts and note that all blocks have tiny Penrose staircases on their "horizontal" faces.
In 0:45 we use a more reasonable gravity direction which does not let us make a perpetuum mobile.
Penrose triangles:
youtu.be/YmFDd49WsrY
youtu.be/RPL4-Ydviug
youtu.be/lWbrHAYsQk4
Penrose staircases and triangles is Nil make us wonder whether we could make gravity point downwards and use it to make a perpetuum mobile.
Such gravity does not make much physical sense, but let's try anyway.
Instead of the native geodesic perspective projection that we have been using in most animations, here we use a Poincaré ball-like projection which maps geodesic spheres to spheres, followed by orthogonal projection to 2D.
In 0:00 the gravity points downwards, in 0:15 and 0:30 the projection is rotated by 30 degrees (and there are more balls).
I expected the effect we see here, because there are no horizontal surfaces in Nil with this gravity. See e.g. twitter.com/ZenoRogue/status/1187378654470430720 or youtu.be/HeFyuVs-Tts and note that all blocks have tiny Penrose staircases on their "horizontal" faces.
In 0:45 we use a more reasonable gravity direction which does not let us make a perpetuum mobile.
Penrose triangles:
youtu.be/YmFDd49WsrY
youtu.be/RPL4-Ydviug
youtu.be/lWbrHAYsQk4
