Category Archives: Anamorphosis

Apollonian gasket as a spherical fractal with tetrahedral symmetry

Before discussing the relation between the Apollonian gasket and tilings of the sphere, I want to present briefly the spherical kaleidoscope with tetrahedral symmetry. A tetrahedron has three different kinds of points with rotational symmetry. Four equilateral triangles make up … Continue reading

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Inversion in a single circle

You might think that discussing the inversion in a circle is somewhat underwhelming. But, as I am using multiple inversion in many circles to create fractal images, I found that there are some important ideas you will not find so … Continue reading

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Various projections of hyperbolic kaleidoscopic images

Similarly to the earlier post “Different projections of spherical kaleidoscopic images” I am now showing the same kaleidoscopic image using different projections you can use in my kaleidoscope browser app http://geometricolor.ch/sphericalKaleidoscopeApp.html. It primarily generates images as Poincaré discs. A typical result … Continue reading

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Double spirals

In the post “Spirals” I have shown how to transform periodic Euclidean tilings into logarithmic spirals. A typical result looks like that: The spiral has a center at the origin and goes out forever. Actually, it spirals not only around … Continue reading

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Different projections of spherical kaleidoscopic images

As you are here, I suppose that you might be interested in the TilingBot living on twitter. Each day it posts the image of a new tiling. Have a look at https://twitter.com/TilingBot and become its follower. I have fun to recognize … Continue reading

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further wallpapers for hyperbolic space

An equilateral triangle gives us a kaleidoscope of three-fold rotational symmetry. With a square we get two-fold rotational symmetry. Would reflection at the sides of other regular polygons too give periodic images with rotational symmetry ? To get an h-fold … Continue reading

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How to program fast kaleidoscopes

This post repeats parts of earlier posts but I am trying to expand the ideas and explain them better. First, I am showing you how to make rosettes with rotational symmetry and mirror symmetry. This is easier than making kaleidoscopic images, … Continue reading

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