Parameterized curve as attractors of some countable iterated function systems

Nicolae-Adrian Secelean

Archivum Mathematicum (2004)

  • Volume: 040, Issue: 3, page 287-293
  • ISSN: 0044-8753

Abstract

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In this paper we will demonstrate that, in some conditions, the attractor of a countable iterated function system is a parameterized curve. This fact results by generalizing a construction of J. E. Hutchinson [Hut81].

How to cite

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Secelean, Nicolae-Adrian. "Parameterized curve as attractors of some countable iterated function systems." Archivum Mathematicum 040.3 (2004): 287-293. <http://eudml.org/doc/249306>.

@article{Secelean2004,
abstract = {In this paper we will demonstrate that, in some conditions, the attractor of a countable iterated function system is a parameterized curve. This fact results by generalizing a construction of J. E. Hutchinson [Hut81].},
author = {Secelean, Nicolae-Adrian},
journal = {Archivum Mathematicum},
keywords = {Hausdorff metric; countable iterated function system; attractor; Hausdorff metric},
language = {eng},
number = {3},
pages = {287-293},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Parameterized curve as attractors of some countable iterated function systems},
url = {http://eudml.org/doc/249306},
volume = {040},
year = {2004},
}

TY - JOUR
AU - Secelean, Nicolae-Adrian
TI - Parameterized curve as attractors of some countable iterated function systems
JO - Archivum Mathematicum
PY - 2004
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 040
IS - 3
SP - 287
EP - 293
AB - In this paper we will demonstrate that, in some conditions, the attractor of a countable iterated function system is a parameterized curve. This fact results by generalizing a construction of J. E. Hutchinson [Hut81].
LA - eng
KW - Hausdorff metric; countable iterated function system; attractor; Hausdorff metric
UR - http://eudml.org/doc/249306
ER -

References

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  1. Barnsley M. F., Fractals everywhere, Academic Press, Harcourt Brace Janovitch, 1988. (1988) Zbl0691.58001MR0977274
  2. Falconer K. J., The Geometry of Fractal Sets, Cambridge University Press, 85, 1985. (1985) Zbl0587.28004MR0867284
  3. Hutchinson J., Fractals and self-similarity, Indiana Univ. Math. J. 30 (1981), 713–747. (1981) Zbl0598.28011MR0625600
  4. Secelean N. A., Countable Iterated Fuction Systems, Far East J. Dyn. Syst., Pushpa Publishing House, vol. 3(2) (2001), 149–167. MR1900096

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