0000000000514631
AUTHOR
Hicham Bensoudane
Tangents to fractal curves and surfaces
International audience; The aim of our work is to specify and develop a geometric modeler, based on the formalism of iterated function systems with the following objectives: access to a new universe of original, various, aesthetic shapes, modeling of conventional shapes (smooth surfaces, solids) and unconventional shapes (rough surfaces, porous solids) by defining and controlling the relief (surface state) and lacunarity (size and distribution of holes). In this context we intend to develop differential calculus tools for fractal curves and surfaces defined by IFS. Using local fractional derivatives, we show that, even if most fractal curves are nowhere differentiable, they admit a left and…
Tangentes à une courbe fractale
http://www.irit.fr/REFIG/index.php/refig/article/view/10; National audience; Nous nous intéressons au calcul des tangentes à une courbe fractale définie à l'aide d'un IFS. Généralement, les courbes fractales sont nulle part dérivables, mais sous certaines conditions on peut montrer qu'elles admettent, en un ensemble de points, des demi-tangentes à droite et à gauche. Nous proposons une méthode permettant de déterminer ces demi-tangentes.
The Local Fractional Derivative of Fractal Curves
Fractal curves described by iterated function system (IFS) are generally non-integer derivative. For that we use fractional derivative to investigate differentiability of this curves. We propose a method to calculate local fractional derivative of a curve from IFS property. Also we give some examples of IFS representing the slopes of the right and left half-tangent of the fractal curves.