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Category Archives: Kaleidoscopes
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
Posted in Anamorphosis, Kaleidoscopes, programming, Tilings
Tagged inversion, inversion in a circle, mirror symmetry
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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
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
Posted in Anamorphosis, Kaleidoscopes, Tilings
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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
Posted in Anamorphosis, Kaleidoscopes
Tagged cuboctahedron, mercator, orthographic projection, sphere, stereographic projection
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Antialiasing for improving image quality
About a year ago I have briefly shown in my post “smoothing images” that averaging can be important to get good images without pixel noise. For my kaleidoscope app, see http://geometricolor.ch/sphericalKaleidoscopeApp.html, I have improved on these ideas and that’s what … Continue reading
Posted in Kaleidoscopes, programming
Tagged antialiasing, image processing, smoothing images
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Bridges 2018 Stockholm
I have been at the Bridges 2018 conference in Stockholm to present my work on kaleidoscopes. My paper “Kaleidoscopes for NonEuclidean Space” has more details than this blog and is more coherent. The Bridges Organization, which promotes connections between mathematics … Continue reading
Straight lines in elliptic and hyperbolic space
A straight line is the shortest path between two points. Discussing curved space we would better call them geodesic lines to avoid confusion. I want to discuss these geodesic lines for surfaces of a sphere, elliptic space and hyperbolic space. … Continue reading
Posted in Kaleidoscopes, programming
Tagged elliptic geometry, geodesic line, hyperbolic geometry, Poincaré disc, straight line
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