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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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Monthly Archives: October 2012
Periodic and quasiperiodic images from crosssections of 4dimensional space
In the earlier post “Quasiperiodic designs from waves and higher dimensional space” I have shown that the quasiperiodic wave pattern with 8fold rotational symmetry is a special crosssection of a periodic pattern in 4dimensional space. Here I will rotate the … Continue reading
Design from waves with tenfold rotational symmetry using another color model
Instead of controlling directly the color components red, green and blue with the waves we can use the huesaturationbrightness color model. In this example the waves of lowest frequency change the brightness. Waves of higher frequency change the hue. Saturation … Continue reading
Posted in Quasiperiodic design
Tagged Color, Quasiperiodic design, Quasiperiodicity, Rotational symmetry
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7 and 14fold rotational symmetry from waves
Similarly as for 5 and 10fold rotational symmetry, see “quasiperiodic design with fivefold rotational symmetry …“, we can create designs with 7 and 14fold rotational symmetry. Here are some examples: In comparison we get here larger round, mandalalike motivs around … Continue reading
Another design with tenfold rotational symmetry from waves
For tenfold rotational symmetry it is quite natural to begin with ten rhombs and angles of 36 degrees. This gives a larger rosette of rhombs than in the post before. The quasiperiodic design I get depends strongly on the choice … Continue reading
Quasiperiodic design with fivefold rotational symmetry in color
An easy way to get color is using three different sets of waves to control the three basic colors red, green and blue. The green color is the brightest one and thus used for the waves of lowest frequencies. The … Continue reading
Quasiperiodic designs from waves and higher dimensional space
I am doing it again – a rather mathematical post. Well, in “An easy way to quasiperiodic tilings” I have shown how to make the AmmannBeenker tiling using two square grids. Then in “How to find these corner points of … Continue reading
A tiling with squares and triangles only
One can go to the other extreme and find suitable dissections of the square and the equilateral triangle without rhombs. For the square we get two different compositions of the sides. Thus we need two different kinds of triangles to … Continue reading