Rotating Snakes Study

Abstract

I was very impressed by Akiyoshi Kitaoka's rotating snakes illusion and needed an extremely high-res version for large printing. After experimenting with more ideas, I ended up with a color-controlled version with a Möbius inverted Doyle spiral and an Apollonian gasket style fractal construction.

Snake Elements

I started by constructing a simple element using two colors from the HSV color wheel. Each snake element has two colors with a constant hue shift. However, the illusion’s effectiveness varies due to the different luminances of the colors.

Basic snake elements.

Color Control

Lea Atala-Gérard and Michael Bach’s work on the rotating snakes illusion shows that the illusion is driven by luminance. I built a computational map to optimize the colors for the strongest illusion effects based on their findings.

The white line indicates 60% luminance, and the black line 20% luminance—these are the colors required for maximal optical illusion effects.

Snake elements with optimized luminance arranged in a hexagonal lattice.

Arrangements

Any circle packing can be used for this, though I chose a Doyle spiral mapped through a conformal Möbius mapping.

A Doyle spiral mapped by a (conformal) Möbius map.

To fill in the gaps, I used Apollonian gasket style fractal packing, adding a circle between every triplet of touching circles recursively for a few generations.

Apollonian gasket style fractal packing.

Variations

By altering parameters such as the number of "spokes" and thickness of the layers, I created several variations that adjust the twist and detail of the illusion.

Various snake element arrangements with different levels of twist.

Why?

For fun—and I wanted some unique decoration.

Printed on nylon fabric.

About Copyright

Do what you want!

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