Numerics and Fractals
Michael F. Barnsley
Vol. 9 No. 3 (2014) P.389~P.430
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.
Iterated function system, local iterated function system, attractor, code space, fractal function, fractal imaging, fractal compression, subdivision schemes.
MATHEMATICAL SUBJECT CLASSIFICATION 2010
Primary: 28A80, 33F05, 41A05, 65D05.
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Revised : 2014-08-06