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Category Archives: Anamorphosis
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 mfold 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
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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A hyperbolic kaleidoscope
In “creating symmetry” Frank Farris shows a wallpaper for hyperbolic space. He uses the Poincaré plane to project the hyperbolic space to our Euclidean drawing surface. The wallpaper then results from mirror symmetries at vertical lines at x=0 and x=0.5 … Continue reading
Posted in Anamorphosis, Kaleidoscopes
Tagged hyperbolic space, inversive geometry, kaleidoscope, mirror symmetry, Poincaré plane
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Five fold rotational symmetry: Tuning the harmonics
In “better images from higher harmonics ?” I have replaced the basic sine and cosine functions by Fourier series approaching a symmetric triangular wave. This gave images with more details and somewhat smaller bullseyes. Here I want to show similar results … 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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