Numerics and Fractals

Abstract

Local iterated function systems are an important generalisation of the standard (global) iterated function systems (IFSs). For a particular class of mappings, their fixed points are the graphs of local fractal functions and these functions themselves are known to be the fixed points of an associated Read-Bajactarević operator. This paper establishes existence and properties of local fractal functions and discusses how they are computed. In particular, it is shown that piecewise polynomials are a special case of local fractal functions. Finally, we develop a method to compute the components of a local IFS from data or (partial differential) equations.

version 2: minor updates and section 6.1 rewritten, arXiv admin note: substantial text overlap with arXiv:1309.0243. text overlap with arXiv:1309.0243