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 discover and 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.
Artworks
Complex Ginzburg-Landau equation on the hyperbolic orbifold (3222)
The Ginzburg-Landau equation describe various non-linear phenomena near bifurcation point. Here we run a simulation of the equation
on the hyperbolic orbifold 3222 (one cone point of order 3 and three cone points of order 2). The solution on the orbifold naturally extends to
the smooth solution in the whole hyperbolic plane. It generates seamless animated symmetric pattern. The hyperbolic plane is represented in conformal band model.
The link to the video https://youtu.be/YdP0W0eRUQc
Gray-Scott Reaction Diffusion the hyperbolic orbifold (3222)
Gray-Scott reaction diffusion is a model of chemical reaction of two reagents. It is represented
as a system of two nonlinear PDE for concentrations of reagents.
We run simulation of the equation on the hyperbolic orbifold 3222.
The solution on the orbifold of finite size smoothly extends to the suymmetric solution in the whiole hyperbolic plane.
The finite size of the orbifold restrict the behavior of the solution and encourages creaton of periodic regime.
link to the video
https://youtu.be/ot_VIVl6SiU
The pattern on the bracelets is build in the Poincare disk model of the hyperbolic plane.
The pattern is converted into infinite band using conformal Mercator projection of the disk.
The appropriate direction of the Mercator projection is chosen to wrap pattern seamlessly
around the finite ring.
-24-09-01-18-05_1.jpg&w=1536&q=75)
-24-09-02-15.jpg&w=1536&q=75)
