Vladimir Bulatov

3D graphics researcher
Corvallis, Oregon

My original training is in physics and math. My artistic passions are purely mathematical images and sculptures, which I are like photographs of mathematical ideas,
which I try to discover and to bring to the real world. I have always been intrigued
by the possibility of showing the intrinsic richness of the mathematical world,
whose visual charm and harmony can really be appreciated by everyone.

Tetrahedral Limit Set
Tetrahedral Limit Set
20 x 20 x 20 cm
plastic, 3D printed

The piece is made using generalized kaleidoscope which in addition to reflections in flat mirrors uses inversions in spherical mirrors. The 5 generalized mirrors (3 flat and 2 spherical) are arranged according to the symmetry of tetrahedron. The interaction of all possible reflections creates tiling of the whole 3D space with conformally identical curved chambers. The curvature of the mirrors causes the size of chambers to shrink to zero near some area of the space. This area is called the limit set of the kaleidoscope. The limit set may have very complex self similar fractal structure. 3D printing is the only way to convert the math into physical object. 3D modeling was done using ShapeJS scripting engine.