The top-selling multimedia encyclopedia Encarta, published by Microsoft Corporation, includes on one CD-ROM seven thousand color photographs which may be viewed interactively on a computer screen.â€¦ (More)

We 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 anyâ€¦ (More)

Chaotic dynamics can be used to model shapes and render textures in digital images. This paper addresses the problem of how to model geometrically shapes and textures of two dimensional images usingâ€¦ (More)

The main theorem of this paper establishes conditions under which the â€˜chaos gameâ€™ algorithm almost surely yields the attractor of an iterated function system. The theorem holds in a very generalâ€¦ (More)

This paper contains four main results associated with an attractor of a projective iterated function system (IFS). The first theorem characterizes when a projective IFS has an attractor which avoidsâ€¦ (More)

A simple, yet unifying method is provided for the construction of tilings by tiles obtained from the attractor of an iterated function system (IFS). Many examples appearing in the literature in adâ€¦ (More)

N ature and evolution provide the notion of a creative system: a core stable form (DNA), a fertile environment, a determination to survive, and random stimuli. Analogously, the mind of aâ€¦ (More)