Blending tilings

Using semitransparent color to superpose tilings does not work out well because it is too difficult to control. Now I have a better idea. Simply draw the tilings as before. Then blend the pictures pixel by pixel by interpolating their color values.

Here I use the Ammann-Beenker tiling with twofold color symmetry as discussed earlier. Different numbers of iteration give the tiling at different scales. The pixel interpolation depends on the horizontal position.

In the first example the difference is just one step of iteration. Thus we see how the iteration proceeds.

This shows the iteration of the Ammann-Beenker tiling. Left and right differ by one step.

The second example demonstrates the self-similarity. The pictures at left and right differ by two steps. With the blending we see how the corner points of one tiling correspond to the stars of rhombs of the other one.

Self-similarity of the Ammann-Beenker tiling.

Blending could also be useful to show the equivalence of two different tilings.

This entry was posted in Self-similarity, Tilings and tagged , , , . Bookmark the permalink.

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