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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: ornament
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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Playing around with the kaleidoscope
You can do things with the computer kaleidoscope you would not try with a real one. Simply look again through the kaleidoscope at an earlier image of the kaleidoscope. Using different scales I got thus:
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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Basic parity rule – sample images
To get smoother images I first use Gaussblur and then a threshold filter. Here I am showing results for the parity rule on the hexagonal lattice with the von Neumann neighborhood. You get more details in my earlier post “The … Continue reading
Twist again
Often, mirrorsymmetric figures are too static for my taste. I prefer pure rotational symmetry. Thus I added to the growth method of the last post a new tip growth step. It changes growth directions by an angle of 45 degrees, … Continue reading
Ornaments of fourfold rotational symmetry
As mentioned in “The benefit of programming mistakes” I am trying to simulate the growth of snow crystals using a modified cellular automaton. Cellular automatons are used in Conway’s game of life and as morphological filters in digital image processing. But … Continue reading
Posted in Cellular automata
Tagged generative design, ornament, Rotational symmetry, Selfsimilarity
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