Wada Fractals Expo

Inspired by Paul Bourke's page about rendering Wada-type basins of attraction.

The basic setup is four identical, highly reflective balls sitting is a pyramid formation so that each ball touches every other ball. One looks into the gaps between three balls and either shines light into all or one of the other gaps or places coloured paper over the gaps and shines light into the same gap one is looking into (or variations of the above). The resulting multitude of reflections, fractal, has what is known as the Wada property after the Japanese mathematician who studied these spatial divisions in 1917. The Wada property refers to cases when there are three basins of attractions so convoluted that every point on a basin boundary is also on the boundary of all other basins.

You can do the real experiments yourself by getting 4 Christmas tree balls or other shiny balls, placing coloured paper over some of the gaps and/or shining light into the gaps. Unfortunately the physical experiment can't be exactly replicated with rendering software because raytracers don't trace light from the light sources back to the camera, rather they trace "fake" rays from the camera back into the scene and finally to the lights.

Wada fractals made with Vivid:
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Wada fractals made with PolyRay:

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Some Wada-type related fractal links:

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