Fractal Tilings from Iterated Function Systems

Fractal Tilings from Iterated Function Systems

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 ad hoc ways, as well as new examples, can be constructed by this method. These tilings can be used to extend a fractal transformation defined on the attractor of a contractive IFS to a fractal transforma...

Fractal image compression and recurrent iterated function systems

ractal geometry provides a basis for modF eling the infinite detail found in nature. Fractal methods are quite popular in computer graphics for modeling natural phenomena such as mountains, clouds, and many kinds of plants. Linear fractal models such as the iterated function system (IFS), recurrent iterated function system (RIFS), and Lindenmeyer systern (L-system) concisely describe complex ob...

Dual Systems of algebraic iterated function systems, Rauzy fractals and β-tilings

Algebraic GIFS is a class of graph-directed iterated function systems (IFS) on R with algebraic parameters. A dual IFS of an algebraic GIFS can be constructed, and the duality between the two systems and has been investigated from various points of view. We review the results of dual IFS concerning the open set condition, purely periodic codings and the Rauzy-Thurston tilings, and their relatio...

On Self‐Affine and Self‐Similar Graphs of Fractal Interpolation Functions Generated from Iterated Function Systems

This chapter provides a brief and coarse discussion on the theory of fractal interpolation functions and their recent developments including some of the research made by the authors. It focuses on fractal interpolation as well as on recurrent fractal interpolation in one and two dimensions. The resulting self-affine or self-similar graphs, which usually have non-integral dimension, were generat...

Iterated Functions Systems and Fractal Coding