%0 Journal Article
%T Numerics and Fractals
%A Michael F. Barnsley
%A Markus Hegland
%A Peter Massopust
%J Mathematics
%D 2013
%I arXiv
%X 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-Bajactarevi\'c 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.
%U http://arxiv.org/abs/1309.0972v3