Get 4 large shiny Christmas balls, some coloured wrapping paper, some lights from the Christmas tree, and you have you own fractal laboratory to amuse yourself with over the festive season.
The basic setup is four identical, highly reflective balls sitting is a pyramid formation so that each ball touches every other ball. You can look into the gaps between three balls and either shines light into all or one of the other gaps or places colored paper over the gaps and shines light into the same gap one is looking into (or variations of the above). The resulting 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.
1 comment:
wow, this is a really interesting concept... those materials are pretty readily available these days... and you can find them on the curb in a week or so and make huge fractal displays for new years!
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