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 A rosette in a roman mosaic is an exponential transform of a periodic tiling
 Fractal tiling of a sphere with octahedral twocolour symmetry
 A fractal tiling of both octahedral and icosahedral symmetry
 A variant of the Apollonian gasket with icosahedral symmetry
 Apollonian gasket as a fractal in tiled hyperbolic space
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Tag Archives: Geometry
Curves
Frank Farris begins his book “Creating Symmetry” with symmetric curves of Nfold rotational symmetry. An example: He uses that we can interpret points (x,y) of the plane as complex numbers z=x+i*y. Thus a complex function f(t) of a real parameter t defines … Continue reading
Posted in Kaleidoscopes, programming
Tagged generative design, Geometry, ornament, Rotational symmetry
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Creating Symmetry
Recently I found a very exciting book: “Creating Symmetry – The Artful Mathematics of Wallpaper Patterns” by Frank A Farris. It has many beautiful images and explains the mathematics behind them very well, such that you could do your own work. His … Continue reading
Posted in Kaleidoscopes, Tilings
Tagged Art, generative design, Geometry, kaleidoscope, symmetry
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Geometry of kaleidoscopes with periodic images
About a year ago I explained “how to program an ideal kaleidoscope” to get the same as three mirrors put together. Often, one gets images that are not periodic. They have cut lines with a mismatch between the two sides, … Continue reading
Posted in Kaleidoscopes
Tagged Geometry, kaleidoscope, mirror symmetry, period doubling, periodic images, Rotational symmetry
2 Comments
improved class Vector – the code
// a class for twodimensional vectors, similarly as PVector, with extensions for complex numbers //———————————————————— // // some important values float vectorSmall=0.0001; float vectorDiameter=8; color vectorColor=color(255); // and here’s the class class Vector{ float x,y; // … Continue reading
improving the class Vector
I am not happy with my class Vector. Looking at my posts “Nautilus” and “selfsimilar fractals …” I realize that complex numbers and vectors should be put together with their methods, which are mostly mappings of the plane. In particular, … Continue reading
high resolution images with offscreen drawing
In an earlier post I have shown how to make smooth images at any scale using the pdfrenderer. But you can do this only with graphics objects such as line, point, shape, ellipse and so on. It won’t work if … Continue reading
Posted in Anamorphosis, Cellular automata, Extra, Fractals, Kaleidoscopes, programming
Tagged Geometry, image resolution, pixel, processing, programming, smoothing images
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tired of rhombs ?
Just only rhombs may become tiring. You want to have a quasiperiodic tiling of tenfold rotational symmetry with other tiles ? Well, we can easily find a different decoration of a tiling such as the one shown in “Dualization method … Continue reading
Posted in Quasiperiodic design, Tilings
Tagged Geometry, ornament, Penrose tiling, programming, quasiperiodic Tiling, rose window
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