Vladimir Bulatov,
Shapeways
Joint AMS/MAA meeting
San Diego, January 10, 2018
Region on the right looks like two components region, however it is an infinite cheese wedge with a spherical hole.
The main feature of hyperbolic tilings visualization is high range of visual scale.
In the circle model of `H^2` we have few regular sized tiles near the center. Tiles shrink rapidly as we approach the horizon.
Upper half plane model `H^2` has similar behavior. Tiles shrink rapidly as we approach the horizon and stretch rapidly as we move up.
Let's "flatten" the hyperbolic plane.
Let's "flatten" the hyperbolic plane.
Let's "flatten" the hyperbolic plane.
We got horosphere.
Zooming out the camera.
Zooming out the camera.
Zooming out the camera.
Zooming out the camera. Animaton https://youtu.be/u1Lp9NS98E0
Slicing euclidean tiling wih plane also produces interesting results