Morphing the tiling of octagons and squares in space

Morphing the periodic tessellation of squares and octagons. It has four-fold rotational symmetry.

An animated morphing of quasiperiodic tilings passes perhaps too rapidly. As tilings repeat throughout space it is quite natural to show their morphing depending on the position in  space or on the computer screen. This we can examine more easily. Here we morph the tiling of octagons and squares. This I have discussed earlier and shown as an animation. For reference I am also showing the morphing of the periodic tessellation. I use a linear interpolation and thus regular octagons appear below the middle of the screen at around 30% (or more exactly 1-sqrt(0.5)) of the height of the image. The dualization method gives then the morphing of the doubled tiling. At the top there is the Ammann-Beenker tiling. Below the middle we see the tiling of octagons and squares. Finally, at the bottom there is again the Ammann-Beenker tiling, but now with a coloring derived from the checkerboard pattern.

Morphing the quasiperiodic tiling of octagons and squares. It has eight-fold rotational symmetry.

This picture makes me think of the great artist M.C. Escher.

 

 

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