"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/