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 A rosette in a roman mosaic is an exponential transform of a periodic tiling
 Fractal tiling of a sphere with octahedral twocolour symmetry
 A fractal tiling of both octahedral and icosahedral symmetry
 A variant of the Apollonian gasket with icosahedral symmetry
 Apollonian gasket as a fractal in tiled hyperbolic space
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Tag Archives: anamorphosis
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 krotational symmetry for an angle of intersection of π/k. With these symmetries I map any point … Continue reading
Posted in Anamorphosis, Kaleidoscopes
Tagged anamorphosis, kaleidoscope, mirror symmetry, rosette, Rotational symmetry
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Morphing between square symmetry and eight fold rotational symmetry
A long time ago in “Crazy graph paper” I have shown a morphing between the square lattice and the quasiperiodic AmmannBeenker tiling of eightfold rotational symmetry. We can do similar morphs with mapping functions using waves. The wave vectors (1,0) … Continue reading
Selfsimilarity and color modification
The Penrose tiling is selfsimilar as many other quasiperiodic tilings. It matches a copy of itself inflated by the golden ratio τ=(1+√5)/2≅1.618, see “Penrose tiling tied up in ribbons“. Noting that our quasiperiodic designs of 5fold symmetry are closely related to … Continue reading
Spirals
Spiral designs are attractive and we can easily get them by transforming periodic designs. An example is the “Iris Spiral” created by Frank Farris. In my earlier post “Nautilus” I tried to explain the method and showed some results. Unfortunately, … Continue reading
Posted in Anamorphosis, Kaleidoscopes
Tagged anamorphosis, kaleidoscope, Rotational symmetry, spiral
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Better images from higher harmonics ?
Maybe you have noticed that a lot of round shapes without details in the recent images of this blog. They resemble bullseyes. Here is an example: It’s a periodic image with square symmetry and no mirror symmetry. Its big grey … Continue reading
Posted in Anamorphosis, Kaleidoscopes, programming
Tagged anamorphosis, kaleidoscope, programming
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2color mirror symmetry
We now want an image with periodic or quasiperiodic rotational symmetry that changes colors upon mirroring. Thus we need a colorchanging function U(x,y) that changes the sign U(x,y)=U(x,y) for its mirror image at the xaxis. We can easily get this … Continue reading
Mirror symmetry and rotational symmetry
To study mirror symmetry at the xaxis together with rotational symmetry we can do similarly as in the earlier post “improved symmetric sum“. Here I prefer to present only the conclusions, which you could get by intuition too. It is important … Continue reading