2024 Joint Mathematics Meetings
Vladimir Bulatov
Artists
Vladimir Bulatov
Mathematics and Arts Explorer
Corvallis, Oregon
Statement
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
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. The goal of this project is to explore solutions of Gray-Scott PDE with wallpaper symmetries. In order to find symmetrical solutions of the PDE we solve it on the orbifold which corresponds to the symmetry group. The solution on the orbifold naturally extends to the symmetrical solution in the whole plane.
Here we represent a video with few such solutions with different wallpaper symmetry groups.
The symmetrical solutions give a nice example of interplay between destructive forces of chaos, spontaneous pattern formation and the restrictive forces of symmetry.