"Monarch Safye"

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).

Reference : Bouali S. (1999), Feedback Loop in Extended van der Pol's Equation Applied to an Economic Model of Cycles, International Journal of Bifurcation and Chaos, Vol. 9, 4, pp. 745-756.

Safieddine Bouali, Assistant Professor in Economics, Management Institute, Quantitative Methods & Economics Department, University of Tunis
Tunis, Tunisia.

"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… "