Tag Archives: ornament

Curves

Frank Farris begins his book “Creating Symmetry” with symmetric curves of N-fold 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

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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:

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tired of rhombs ?

Just only rhombs may become tiring. You want to have a quasiperiodic tiling of ten-fold 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

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Basic parity rule – sample images

To get smoother images I first use Gauss-blur 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

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Twist again

Often, mirror-symmetric 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

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Ornaments of four-fold 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

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