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Category Archives: Tilings
Decorations of semiregular tessellations
In the last posts I have shown kaleidoscopes that make repeating images in Euclidean, spherical and hyperbolic spaces. They are decorations of regular tilings. But what about semiregular tilings? Could we decorate them too using mirrors? This would give us … Continue reading
Posted in Kaleidoscopes, Tilings
Tagged hexagonal lattice, kaleidoscope, mirror symmetry, Tessellation
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further wallpapers for hyperbolic space
An equilateral triangle gives us a kaleidoscope of threefold rotational symmetry. With a square we get twofold rotational symmetry. Would reflection at the sides of other regular polygons too give periodic images with rotational symmetry ? To get an hfold … Continue reading
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
improved combination of color symmetry and rotation
As mentioned in the last post using two unrelated anamorphic mappings, one for reading the input image and another one for choosing color variants, makes it difficult to create interesting images. From the mapping that determines the color variant we … Continue reading
threecolor rotational symmetry
I found it rather difficult to add threecolor symmetry to rotational symmetry and had to do the theory of the post “color symmetry upon rotation“. Then, programming was quite easy. In the end we combine a periodic or quasiperiodic anamorphic … Continue reading
twocolor rotational symmetry
We can only add a twocolor symmetry to a rotational symmetry if the rotational symmetry is of even order. After some simple calculations, we get from the previous post a real mapping for selecting the color variants where the d … Continue reading
Improved symmetric sum
I’ve found a better way how to write the sums of the posts “Rotational symmetry from space with an odd number of dimensions” and “Rotational symmetry from space with an even number of dimensions“. It is more compact, shows how to calculate … Continue reading
Posted in Anamorphosis, Kaleidoscopes, Quasiperiodic design, Tilings
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