Bilinear fractal interpolation and box dimension

In the context of general iterated function systems (IFSs), we introduce bilinear fractal interpolants as the fixed points of certain Read–Bajraktarević operators. By exhibiting a generalized “taxi-cab” metric, we show that the graph of a bilinear fractal interpolant is the attractor of an underlyin...

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Bibliographic Details
Published in:Journal of approximation theory 2015-04, Vol.192, p.362-378
Main Authors: Barnsley, Michael F., Massopust, Peter R.
Format: Article
Language:English
Subjects:
Attractor
Bilinear IFS
Bilinear mapping
Box counting dimension
Fractal interpolation
Iterated function system (IFS)
Read–Bajraktarević operator
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Summary:In the context of general iterated function systems (IFSs), we introduce bilinear fractal interpolants as the fixed points of certain Read–Bajraktarević operators. By exhibiting a generalized “taxi-cab” metric, we show that the graph of a bilinear fractal interpolant is the attractor of an underlying contractive bilinear IFS. We present an explicit formula for the box-counting dimension of the graph of a bilinear fractal interpolant in the case of equally spaced data points.
ISSN:0021-9045
1096-0430
DOI:10.1016/j.jat.2014.10.014