Tag Archives: anamorphosis

Quasiperiodic design with 8-fold rotational symmetry from 4-dimensional space

Using the recipe of the last post for four-dimensional space (p=4) I got this image of 8-fold rotational symmetry: A center of approximate 8-fold rotational symmetry is near the lower left corner. Large brown patches appear at roughly equal distances. … Continue reading

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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

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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

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quasiperiodic patterns of 5-fold 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 5-fold symmetry … Continue reading

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n-fold 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

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rosettes with glide reflection

For a rosette of p-fold 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

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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

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