Dr. Jozsef Vass, York University
“A Constructive Approach to the Convex Hull of IFS Fractals in the Plane, and its Generalization”
Determining the extremal points of IFS fractals, is both an intriguing theoretical problem which may serve the resolution of other theoretical questions, as well as a practical tool for computational geometric algorithms. Former results address the special case of self-affine tiles via eigenvectors of powers of the scaling matrix, however an alternate novel approach is necessary for the broader class of similitude IFS fractals. We show the finiteness of extrema for the special though quite general planar subclass of ”fractals of unity”, along with the constructive determination of their convex hull. The overall technique, as well as the steps to be overcome in the generalization of this convex hull determination method beyond the plane, will be hereby addressed. The method builds upon the work of Wang, Kirat, and Mandelbrot et al. The latter’s work on self-contacting fractal trees highlights the relevance of the loci of extrema to the much-researched problem of connectedness.
MC 5479