Category Archives: Anamorphosis

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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Elliptic kaleidoscopes

In “further hyperbolic kaleidoscopes” I used two straight lines and a circle to make a triangle that defines a kaleidoscope. For k,n and m-fold rotational symmetries at its corners, the sum of its three angles is π(1/k+1/n+1/m). If this sum is … Continue reading

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The rotational and mirror symmetry at the center

In the last post I used mirror symmetry at two crossing straight lines and the related inversion at a circle. The mirror symmetries generate a k-rotational symmetry for an angle of intersection of π/k. With these symmetries I map any point … Continue reading

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