Four stages of bending M.C.Escher "Circle Limit IV".

The art work for this one was hellishly hard to simulate.

And I even didn't reproduce M.C.Escher original woodcut detail - half of

the angels and half of devils are actually looking back.

The art work for this one was hellishly hard to simulate.

And I even didn't reproduce M.C.Escher original woodcut detail - half of

the angels and half of devils are actually looking back.

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- Cool! It looks like you've discovered a clever new trick for creating infinite numbers of holes in the hyperbolic disk. Are the tiles an exact fit?Jan 23, 2012
- It is the same 3D bending of 2D hyperbolic symmetry group generated by reflections in the sides of quadrilateral

I've described in http://bulatov.org/math/1107

All the tiles are the same and fit perfectly and can be mapped to each other using Moebius transformation.

Angles and devils belongs to 2 different classes though.

All the circular holes in the holed tilings are equivalent (including the largest hole

with the center at infinity - outside of the disk)Jan 23, 2012 - Looks great!Jan 23, 2012
- Great work, Vladimir, thank you!Jan 24, 2012
- This tiling software will blow you away: http://www.gravitation3d.com/magictile/ Rubik style twisty puzzles on hyperbolic surfaces and other topologies. It is as much art as math.Feb 22, 2012
- Yes, this is cool software!Feb 22, 2012