The connection between mathematics and art goes back thousands of years. Mathematics has been used in the design of Gothic cathedrals, Rose windows, oriental rugs, mosaics and tilings. Geometric forms were fundamental to the cubists and many abstract expressionists, and award-winning sculptors have used topology as the basis for their pieces. Dutch artist M.C. Escher represented infinity, Möbius bands, tessellations, deformations, reflections, Platonic solids, spirals, symmetry, and the hyperbolic plane in his works.
Mathematicians and artists continue to create stunning works in all media and to explore the visualization of mathematics--origami, computer-generated landscapes, tesselations, fractals, anamorphic art, and more.
"Monarch Safye," by Safieddine Bouali (University of Tunis, Tunisia)
Digital print, 20" x 24", 2009. Deterministic 3D strange attractor built with the dynamical system:
dx/dt = 0.02 y + 0.4 x ( 0.2 - y2 ) (1)
dy/dt = - x + 35 z (2)
dz/dt = 10 x - 0.1 y (3)
Initial Condition (x0, y0, z0 ) = ( 0, 0.01, 0 ), fifth-order Runge Kutta method of integration, and accuracy = 10-5. Euclidian coordinates representation : ( y, - x, z). I have always been fascinated by the Lorenz Attractor. I like to create and simulate systems of ordinary differential equations on my computer. A simple raylight formed by a 3D model follows intricate dynamics. Visualizing an infinite trajectory drawing elegant attractors within a limited phase of space unravels the aesthetics appeal of the Deterministic Theory of Chaos. Indescriptible happiness when new strange attractors emerge in my computer screen ! These are sculptures of motion. Derived from the Sensitive Dependency on Parameters , an unique chaotic model displays an unpredictable class of attractors. Indeed, from theoretical viewpoint, no relationship between mathematical equations and attractor shapes has ever been found. Chaotic attractors are mysterious figures but reproducible in various media by everyone if mathematical formulas are clearly expressed, I think discovering unexpected strange attractors by the exploration of 3D dynamical models constitutes a full artistic principle. By unconventional ways, I search beauty. --- Safieddine Bouali (University of Tunis, Tunisia) http://chaos-3d.e-monsite.com/