Non-Euclidean Symmetry and Indra's Pearls

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Caroline Series and David Wright: Non-Euclidean Symmetry and Indra's Pearls. In: Bridges 2006. Pages 25–32



Escher’s well known picture of devils and angels is an example of a symmetrical tiling of two dimensional hyperbolic space. We discuss similar symmetries of three dimensional hyperbolic space, modelled as the inside of a solid ball. The ‘shadows’ of the solid tiles on the boundary of the ball themselves form patterns governed by a new kind of symmetry, that of Möbius maps on the complex plane. All aspects of such pictures, together with instructions for making them, are explored in the authors’ book Indra’s Pearls. We give examples of beautiful fractal patterns created in this way.

Extended Abstract


Used References

[1] Indra’s Pearls, The Vision of Felix Klein, D. Mumford, C. Series and D. Wright, Cambridge University Press, 2002.


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