Penguins on the hyperbolic plane:

This is an example of a tesselation of the hyperbolic plane by fundamental domains of a Fuchsian group with cusps. Cusps correspond to yellow/green horodiscs on the picture. You can notice that horocircles are metrically distorted in the hyperbolic plane since the Euclidean size of penguins which live on horocircles is decreasing much slower than the size of penguins which do not live on a common horocircle.



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