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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: programming
Changing the hue
It has been easy to find special color transformations for 2 and 3color symmetries. For other color symmetries I use a rather general color transformation that changes the hue. First, we separate the pixel color in a grey part and … Continue reading
Posted in Kaleidoscopes, programming
Tagged Color, color manipulation, hue, programming
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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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Kaleidoscopes with twofold color symmetry.
A checkerboard is a square lattice with twofold color symmetry. The alternating black and white squares make it more interesting than a simple square lattice. Thus I want to have too some twofold color symmetry for our kaleidoscopes. Farris has done this … Continue reading
Posted in Kaleidoscopes, programming
Tagged color symmetry, kaleidoscope, programming, twocolor symmetry
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Rosettes with mirror symmetry
The program for making rosettes offers many possibilities and it is difficult to find something to aim for. As a guide we can use symmetries. Mirror symmetry at the xaxis is a simple example. It makes that the image remains unchanged … Continue reading
Posted in Anamorphosis, Kaleidoscopes
Tagged image processing, mirror symmetry, programming, rosette, Rotational symmetry
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How to generate rosettes
A rosette is an image with rotational symmetry. For pfold symmetry we can use the methods of the last post “Anamorphosis and symmetries” with a simple power as a mapping function between output and input images: Here z=x+iy relates to … Continue reading
Posted in Anamorphosis, Kaleidoscopes, programming
Tagged anamorphosis, image processing, programming, Rotational symmetry
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Anamorphosis and symmetries
As proposed by Farris in “Creating Symmetry” we can use anamorphosis to make images of any symmetry from some other input image. Here I briefly discuss how I am doing it and what you will find in my next program. Each … Continue reading
Posted in Anamorphosis, Kaleidoscopes, programming
Tagged kaleidoscope, programming, symmetry
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Approximating the logarithm function
I still want fast approximations of the logarithm and the inverse tangent function for my work. I don’t know if they are really needed, but they are nice pillow problems to keep you from ruminating those stupid things happening now. If x is … Continue reading