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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: generative design
Numerical performance
Curves do not need much calculations and are easy to generate. Rosettes, friezes and kaleidoscopes are different. They need many calculations for each pixel, often using several evaluations of trigonometric functions and exponential functions. Fortunately, our PCs are fast. A … Continue reading
Posted in programming
Tagged function evaluation, generative design, numerics, performance, programming, speed
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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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Selfsimilar images from iterated mappings of the plane
A mapping of the plane defines simply another point (u,v) in the plane as a function of the coordinates (x,y) of a point in the plane. The mapping is defined by the functions for the new coordinates u=f(x,y) and v=g(x,y). … Continue reading
cellular automaton with color on a square lattice
I used the same methods as in the last post but now for a square lattice. I could not get similar results with 4fold rotational symmetry instead of 6fold rotational symmetry. Instead, the images were rather different. For my taste, … Continue reading
Posted in Cellular automata
Tagged Cellular automaton, Color, generative design, Moore neighborhood, square lattice
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Hexagonal cellular automaton in color
The images from the hexagonal cellular automaton shown in “Basic parity rule – sample images ” and “Modified parity rule – sample images ” are only black and white. But I prefer color. To get similar images in color I modified the … Continue reading
Modified parity rule – sample images
This is quite similar to the last posts with some small changes: As in the post “The modified parity rule” I am now counting the state of the cell itself too. To get a calmer image I am using gray as … Continue reading
Posted in Cellular automata
Tagged Cellular automaton, generative design, hexagonal lattice
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