Tag Archives: color symmetry

3-color symmetry

For color symmetries we need a mapping W(z) for its structure as discussed in the last post and some suitable color transformations. In an earlier post I discussed some simple transformations for making a 2-color symmetry. For 3-color symmetries we … Continue reading

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n-fold color symmetry

Let’s begin with a simple kaleidoscope, where a pixel at coordinates z=x+iy has the original colors of an input image at the mapped coordinates Z(z)=X(x,y)+iY(x,y). It has some symmetry s. It is a mapping of the plane that does not … Continue reading

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Simple example of a rosette with two-color symmetry

To keep things simple I am creating rosette with six-fold rotational symmetry. The mapping functions are, using polar coordinates: X = r³ cos(6*φ) and Y = r³ sin(6*φ). An input image of a single butterfly results in 6 distorted butterflies: The black … Continue reading

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Kaleidoscopes with twofold color symmetry.

A checkerboard is a square lattice with twofold color symmetry. The alternating black and white squares make it more interesting than a simple square lattice. Thus I want to have too some twofold color symmetry for our kaleidoscopes. Farris has done this … Continue reading

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checkerboard coloring of tiling with 12-fold rotational symmetry

At the risk of boring you I am showing the results of the checkerboard coloring as discussed in the last post, but now for 12-fold rotational symmetry. Again the stars of rhombs have only one color: All squares have the … Continue reading

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checkerboard coloring of quasiperiodic tilings

A long time ago I found a coloring of the rhombs of the Ammann-Beenker tiling using two colors such that translations exchange colors, see “two-fold color symmetry …“. In particular, there are stars of rhombs of both colors. They define … Continue reading

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More magic mirrors

For a kaleidoscope with six-fold rotational symmetry and using three distinct colors I made up a new kind of mirrors that exchanges colors cyclically. That means that color number one becomes color number 2 in the mirror image. Then color … Continue reading

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