Generation of Fractals via Self-Similar Group of Kannan Iterated Function System

Authors

R. Uthayakumar, Department of Mathematics, The Gandhigram Rural Institute, Deemed University, Gandhigram – 624 302, Dindigul, Tamil Nadu, India.Follow
A. Gowrisankar, Department of Mathematics, The Gandhigram Rural Institute, Deemed University, Gandhigram – 624 302, Dindigul, Tamil Nadu, India.Follow

Author Country (or Countries)

India.

Abstract

In this paper, we introduce and investigate some definition and property of self-similar group and strong self-similar group of Kannan contraction. These groups are found as the attractor of a Kannan iterated function system (KIFS). This paper improves the Hutchinson-Barnsley theory in the sense of KIFS. Fractal set can be constructed by self-similar and strong self-similar group in the sense of KIFS of compact topological group. Finally, we prove the relation between profinite group and strong self-similar group of Kannan contraction.

Recommended Citation

Uthayakumar, R. and Gowrisankar, A. (2015) "Generation of Fractals via Self-Similar Group of Kannan Iterated Function System," Applied Mathematics & Information Sciences: Vol. 09: Iss. 6, Article 52.
Available at: https://digitalcommons.aaru.edu.jo/amis/vol09/iss6/52