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 Quasiperiodic design with 8fold rotational symmetry from 4dimensional space
 Rotational symmetry from space with an even number of dimensions
 Periodic design with 3fold rotational symmetry from 3dimensional space
 Inversion symmetry doubles the rotation symmetry for an odd number of dimensions
 quasiperiodic patterns of 5fold symmetry from 5 dimensional space
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Tag Archives: anamorphosis
Quasiperiodic design with 8fold rotational symmetry from 4dimensional space
Using the recipe of the last post for fourdimensional space (p=4) I got this image of 8fold rotational symmetry: A center of approximate 8fold rotational symmetry is near the lower left corner. Large brown patches appear at roughly equal distances. … Continue reading
Rotational symmetry from space with an even number of dimensions
For an embedding space with an even number of dimensions p=2q we do similarly as for an odd number of dimensions, see the earlier post “Rotational symmetry from…“. Note that now we should not use an angle of 2π/p between … Continue reading
Posted in Anamorphosis, Kaleidoscopes
Tagged anamorphosis, kaleidoscope, Rotational symmetry
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Inversion symmetry doubles the rotation symmetry for an odd number of dimensions
We now want to impose inversion symmetry in addition to rotational symmetry on our designs. This means that the mapping functions should not change upon inversion of the position. Thus X(x,y)=X(x,y) and Y(x,y)=Y(x,y). Let’s consider space with an odd number … Continue reading
quasiperiodic patterns of 5fold symmetry from 5 dimensional space
I now want to see some images. Using a photo of a caterpillar as input image I get I used the simplest quasiperiodic mapping functions resulting from the theory of the last post and The center of perfect 5fold symmetry … Continue reading
Posted in Anamorphosis, Kaleidoscopes, Quasiperiodic design
Tagged anamorphosis, Art, Quasiperiodic design, Rotational symmetry
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nfold color symmetry
Let’s begin with a simple kaleidoscope, where a pixel at coordinates z=x+iy has the original colors of an input image at the mapped coordinates Z(z)=X(x,y)+iY(x,y). It has some symmetry s. It is a mapping of the plane that does not … Continue reading
Posted in Anamorphosis, Kaleidoscopes
Tagged anamorphosis, color symmetry, kaleidoscope, programming, Rotational symmetry
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rosettes with glide reflection
For a rosette of pfold rotational symmetry you have an equivalent to the glide reflection symmetry of a fries. It is a rotation by an angle of π/p around its center together with a reflection or rather inversion at r=1. … Continue reading
Posted in Anamorphosis, Kaleidoscopes
Tagged anamorphosis, rose window, Rotational symmetry
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Rosettes with another mirror symmetry
Symmetries are important for design because they determine the overall appearance of an image. Rotational symmetry without mirror symmetry makes a dynamical image, whereas additional mirror symmetries give a more static appearance. Generally, an image becomes more abstract if we … Continue reading
Posted in Anamorphosis, Kaleidoscopes
Tagged anamorphosis, kaleidoscope, mirror symmetry, Rotational symmetry
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