Bilinear fractal interpolation and box dimension

被引：72
|
作者：
Barnsley, Michael F. [1 ]
Massopust, Peter R. [2 ,3 ]
机构：
[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
来源：
JOURNAL OF APPROXIMATION THEORY | 2015年 / 192卷
关键词：
Iterated function system (IFS); Attractor; Fractal interpolation; Read-Bajraktarevic operator; Bilinear mapping; Bilinear IFS; Box counting dimension;
D O I：
10.1016/j.jat.2014.10.014
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
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.
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页码：362 / 378
页数：17
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