If you look inside of four reflective spheres stacked in a tetrahedron you can see a nice fractal image. This is a simplified model of chaotic scattering in a Hamiltonian system with three degrees of freedom (which can be described by a 4D map).

If you stack the spheres in a different geometry, so that each sphere only touches two of the other spheres, then the image below reveals itself. This image is part of current research here in the Maryland Chaos Group.

For more information, see the D. Sweet, E. Ott, J. A. York, Nature 399, 315(1999).

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