Bilinear fractal interpolation and box dimension

Michael F. Barnsley; Peter R. Massopust

doi:10.1016/j.jat.2014.10.014

Bilinear fractal interpolation and box dimension

Michael F. Barnsley
, Peter R. Massopust^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

93 Citations (Scopus)

Abstract

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.

Original language	English
Pages (from-to)	362-378
Number of pages	17
Journal	Journal of Approximation Theory
Volume	192
DOIs	https://doi.org/10.1016/j.jat.2014.10.014
Publication status	Published - 1 Apr 2015

Access to Document

10.1016/j.jat.2014.10.014

Cite this

@article{b5cb682068dd4c6a833b8996be3bbaf0,

title = "Bilinear fractal interpolation and box dimension",

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 = "Attractor, Bilinear IFS, Bilinear mapping, Box counting dimension, Fractal interpolation, Iterated function system (IFS), Read-Bajraktarevi{\'c} operator",

author = "Barnsley, \{Michael F.\} and Massopust, \{Peter R.\}",

note = "Publisher Copyright: {\textcopyright} 2014 Elsevier Inc.",

year = "2015",

month = apr,

day = "1",

doi = "10.1016/j.jat.2014.10.014",

language = "English",

volume = "192",

pages = "362--378",

journal = "Journal of Approximation Theory",

issn = "0021-9045",

publisher = "Academic Press Inc.",

}

TY - JOUR

T1 - Bilinear fractal interpolation and box dimension

AU - Barnsley, Michael F.

AU - Massopust, Peter R.

PY - 2015/4/1

Y1 - 2015/4/1

N2 - 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.

AB - 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.

KW - Attractor

KW - Bilinear IFS

KW - Bilinear mapping

KW - Box counting dimension

KW - Fractal interpolation

KW - Iterated function system (IFS)

KW - Read-Bajraktarević operator

UR - https://www.scopus.com/pages/publications/84923065842

U2 - 10.1016/j.jat.2014.10.014

DO - 10.1016/j.jat.2014.10.014

M3 - Article

SN - 0021-9045

VL - 192

SP - 362

EP - 378

JO - Journal of Approximation Theory

JF - Journal of Approximation Theory

ER -

Bilinear fractal interpolation and box dimension

Abstract

Access to Document

Other files and links

Fingerprint

Cite this