On the Exact Convex Hull of IFS Fractals

Abstract

The problem of finding the convex hull of an IFS fractal is relevant in both theoretical and computational settings. Various methods exist that approximate it, but our aim is its exact determination. The finiteness of extremal points is examined a priori from the IFS parameters, revealing some cases when the convex hull problem is solvable. Former results are detailed from the literature, and two new methods are introduced and crystallized for practical applicability -- one more general, the other more efficient. Focal periodicity in the address of extremal points emerges as the central idea.