Numerics and Fractals
by Michael F. Barnsley   Markus Hegland   Peter Massopust  

Vol. 9 No. 3 (2014) P.389~P.430

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-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.

KEYWORDS
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.

MILESTONES

Received: 2013-11-01
Revised : 2014-08-06
Accepted: 2014-08-05

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