Analysis of fractal dimension of light scattering in polyhedral mirror-ball structures

We experimentally observed fractal patterns in polyhedral mirror-ball structures and analyzed fractal dimension of the basin boundaries by using models. Regular-tetrahedral mirror-ball structures have been already proposed as a chaos mirror and a three-dimensional optical billiard, in which the centers of four spherical reflectors are located at the vertices of a regular tetrahedron. We extended the regular-tetrahedral mirror-ball structure to a regular-hexahedral (cubic) mirror-ball structure. We used a commercially available software for the calculation of the box-counting dimension of the fractal patterns. We found that the fractal dimension increases as the number of surface of the polyhedral structures increases, except dodecahedron.