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 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
 Apollonian gasket as a spherical fractal with tetrahedral symmetry
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Tag Archives: Rotational symmetry
images with 5fold symmetry and color change indicating selfsimilarity
And now for more images with 5fold rotational symmetry and color change derived from selfsimilarity as discussed in “selfsimilarity and color modification“. Zoom in to see the molten watch faces in this image: Here I used the portrait of a … Continue reading
images of 8fold rotational symmetry and color changing mirror symmetry
Here I am showing some quasiperiodic designs of eightfold rotational symmetry. They have a color change upon mirroring at the xaxis and 7 other mirror axis generated by the rotational symmetry. Note that these images have a rather large scale … Continue reading
images of 10fold rotational symmetry and 2color symmetry upon rotation
Here are some images of 10fold rotational symmetry and 2color symmetry upon rotation. They have an additional mirror symmetry. Thus you can discover local mirror symmetries with and without color change. Again, they are of large size and you can … Continue reading
Posted in Quasiperiodic design
Tagged color symmetry, Quasiperiodic design, Rotational symmetry
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Examples of basic fivefold rotational symmetry
Here are some quasiperiodic designs of fivefold rotational symmetry. They relate to the Penrose tiling and use the method of “quasiperiodic patterns of 5fold symmetry …“. For all three images the wave packages for the anamorphic mappings X(x,y) and Y(x,y) use the … Continue reading
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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