Several tools are used to render hyperbolic kaleidoscopes.
One tool is custom java program, which generates set of
symmetry transformations of hyperbolic plane and dumps them in povray or VRML format.
VRML file is used to interactively select starting tile of the kaleidoscope. Interactive VRML kaleidoscopes can be found at my site bulatov.org.
Parameters of starting tile are fed into povray file and are rendered using povray.
Rendered scenes contains about 30,000 tiles.

There are 3 types of 2D geometry - plane, spherical and hyperbolic.
Hyperbolic kaleidoscope - is kaleidoscope on hyperbolic plane.
Popular model of hyperbolic plane is Poincare disk model.
This image is kaleidoscope in disk model of hypebolic plane and
the disk is shrunk inside of hexagon. (3,7) means, that it has
point of symmetry of 3rd and 7th order (and 2nd).
In contrast to normal plane, where only kaleidoscopes of type (3,6) and (4,4) are possible on hyperbolic plane kaleidoscope of all other types (n,m) are possible.
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