# Vladimir Bulatov

Artist

none

Corvallis, OR

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 Sets

5 x 5 x 5 cm each

3D printed steel and bronze composite

2012

The inversive reflection group is symmetry group formed by reflections in planes and inversions in spheres.

The limit set of a such group is set of accumulation of actions of the group on arbitrary initial point. If spheres or planes have kaleidoscopic intersection angles ($\pi/n$) the group is discrete and its limit set can be empty, very simple or very complex.

Simplest example - familiar group formed by reflections in 6 sides of a room with mirror walls floor and ceiling. The limit set of this group has one point - infinity.

Another example. Reflection group formed by 3 intersecting spheres that have 3 intersection angles which form hyperbolic triangle (sum of angles is less than $\pi$). This group is isomorphic to two dimensional hyperbolic triangle groups and its limit set is a circle.

Here are few less simple examples of limit sets of group formed by reflections few spheres and planes. The limit set in these cases has complex self similar fractal structure.

The limit set of a such group is set of accumulation of actions of the group on arbitrary initial point. If spheres or planes have kaleidoscopic intersection angles ($\pi/n$) the group is discrete and its limit set can be empty, very simple or very complex.

Simplest example - familiar group formed by reflections in 6 sides of a room with mirror walls floor and ceiling. The limit set of this group has one point - infinity.

Another example. Reflection group formed by 3 intersecting spheres that have 3 intersection angles which form hyperbolic triangle (sum of angles is less than $\pi$). This group is isomorphic to two dimensional hyperbolic triangle groups and its limit set is a circle.

Here are few less simple examples of limit sets of group formed by reflections few spheres and planes. The limit set in these cases has complex self similar fractal structure.