Bilinear fractal interpolation and box dimension

JOURNAL OF APPROXIMATION THEORY

卷:192

Article

Barnsley, Michael F.¹  Massopust, Peter R.^2,3 

[1] Australian Natl Univ, Inst Math Sci, Canberra, ACT, Australia

[2] Tech Univ Munich, Res Unit M6, Ctr Math, D-85747 Garching, Germany

[3] Helmholtz Zentrum Munchen, D-8764 Neuherberg, Germany

关键词: Iterated function system (IFS);    Attractor;    Fractal interpolation;    Read-Bajraktarevic operator;    Bilinear mapping;    Bilinear IFS;    Box counting dimension;   

DOI  :  10.1016/j.jat.2014.10.014

来源: Elsevier

【 摘 要 】

In the context of general iterated function systems (IFSs), we introduce bilinear fractal interpolants as the fixed points of certain Read Bajraktarevic 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. (C) 2014 Elsevier Inc. All rights reserved.

【 授权许可】

Free