2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/153944We establish properties of a new type of fractal which has partial self similarity at all scales. For any collection of iterated functions systems with an associated probability distribution and any positive integer V there is a corresponding class of V-variable fractal sets or measures. These V-variable fractals can be obtained from the points on the attractor of a single deterministic iterated function system. Existence, uniqueness and approximation results are established under average contractive assumptions. We also obtain extensions of some basic results concerning iterated function systems.33 pages, 3 figuresDynamical SystemsProbability28A80; 37H99; 60G57; 60J05text