Bilinear Fractal Interpolation and Box Dimension
Metric Geometry
2014-10-28 v4
Abstract
In the context of general iterated function systems (IFSs), we introduce bilinear fractal interpolants as the fixed points of certain Read-Bajraktarevi\'{c} 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.
Keywords
Cite
@article{arxiv.1209.3139,
title = {Bilinear Fractal Interpolation and Box Dimension},
author = {Michael F. Barnsley and Peter R. Massopust},
journal= {arXiv preprint arXiv:1209.3139},
year = {2014}
}