A STUDY ON ITERATED FUNCTION SYSTEMS

T. Abirami; M. Suresh Kumar

doi:https://doi.org/10.14445/22315373/IJMTT-V67I12P505

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 67 | Issue 12 | Year 2021 | Article Id. IJMTT-V67I12P505 | DOI : https://doi.org/10.14445/22315373/IJMTT-V67I12P505

A STUDY ON ITERATED FUNCTION SYSTEMS

T. Abirami, M. Suresh Kumar

Citation :

T. Abirami, M. Suresh Kumar, "A STUDY ON ITERATED FUNCTION SYSTEMS," International Journal of Mathematics Trends and Technology (IJMTT), vol. 67, no. 12, pp. 47-56, 2021. Crossref, https://doi.org/10.14445/22315373/IJMTT-V67I12P505

Abstract

In this paper, every metric d on a nonempty set X induces a metric h, called Hausdorff metric, on the set K(X) of the collection of all non-empty compact subsets of X. It is a well known fact that the induced metric preserves the completeness and compactness. In this paper, we discuss the existence of attractors, which is generally known as fractals, of iterated function systems using the Hausdorff metric. We also discuss how to construct the attractors of iterated function systems using the fixed points of contraction maps involved in the iterated function systems.

Keywords

Hausdorff metric, Compact, Complete,Contraction, Iterate Function Systems,Attractor.

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