# Vladimir Bulatov

3D Graphics Researcher

Shapeways

Corvallis, Oregon, USA

My artistic passions are purely mathematical images and sculptures,

which express a certain vision of forms and shapes, my interpretations of distance,

transformations and space. In my opinion, mathematics is a way of thinking, a way of life.

My images and sculptures are like photographs of interesting 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 charm and harmony can really be appreciated by everyone.

which express a certain vision of forms and shapes, my interpretations of distance,

transformations and space. In my opinion, mathematics is a way of thinking, a way of life.

My images and sculptures are like photographs of interesting 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 charm and harmony can really be appreciated by everyone.

Limit Set #170922

20 x 20 x 20 cm

Nylon, glass

2017

M.C.Escher Circle Limit woodcuts are based on symmetry group generated by inversions in 3 circles. Such groups limit set is contained in a circle. Limit set of group generated by inversions in spheres may be much more complicated. 4 generators groups have rather intricate limit set which is always contained in a sphere. 5 or more generators group may have truly three dimensional structure. The calculations of 3D limit set involve reverse mapping of each point in space into fundamental domain of the group. The inverse Jacobian of the transformation is used as measure of distance of point to the limit set. The modeling was done in ShapeJS. Two 3D prints of simplest non trivial cases of groups with 5 generators are presented here.

Limit Set 170923

20 x 20 x 5 cm

Nylon, glass

2017

Limit set of 5 generators reflection group