I first saw Vladimir give a talk in 2010 and his work and images were totally inspiring to me.

I first saw Vladimir give a talk in 2010 and his work and images were totally inspiring to me. That has continued ever since!

Originally shared by Vladimir Bulatov

I've posted slides from my talk on hyperbolic tilings
http://bulatov.org/math/180110

Comments

  1. Hm, he says it's non repeating but the left half looks identical to the right to me.

    ReplyDelete
  2. Melinda Green, it's aperiodic in the same way as a Penrose tiling. That is, a shifted copy of the tiling will never match the original (shift meaning Euclidean translations). Aperiodic Penrose tilings can have reflection symmetry as well, even as much as 5-fold dihedral symmetry.

    ReplyDelete
  3. Roice Nelson But that's exactly how it looks to me. Use your stereo vision to fuse both halves. They look pixel-for-pixel identical to me.

    ReplyDelete
  4. Melinda Green, I see, you're right! Looking through the slides again, I think the title image is not a horosphere section. Not only is it repeating under a translation, the tiles shrink in size instead of remaining constant. I'm guessing Vladimir Bulatov used a section of a hyperbolic plane for the title image.

    ReplyDelete
  5. Melinda Green Roice Nelson is 100% correct. The title image is just pretty looking image. More exactly it is unwrap of cylindrical projection from a surface of a sphere intersecting the tiling inside of Poincare sphere. The region where that sphere intersect the surface of Poincare sphere has tilings of infinitely small size. Therefore we have that illusion of horizon.
    https://lh3.googleusercontent.com/SeSoJxk1Vqlrx55KY3o50Y_84ukXcxG4_mgJyj9dkd5PbLReivWHlF1mNeZ58cckUcRi85FnfFfMhQisAe4i_n4Txm2PNWbNzec=s0

    ReplyDelete
  6. Vladimir Bulatov OK but are the two halves identical or not?

    ReplyDelete
  7. Melinda Green yes, they are identical as tiling has symmetry plane via center of the sphere.

    ReplyDelete

Post a Comment

Popular posts from this blog

Hyperbolic Hopf Fibrations