Journal
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
Volume 67, Issue -, Pages 594-599Publisher
ELSEVIER
DOI: 10.1016/j.cnsns.2018.07.012
Keywords
Hausdorff metric space; Contraction mapping; Self-similarity; Fractal
Ask authors/readers for more resources
Fractal theory is the study of irregularity which occurs in natural objects. It also enables us to see patterns in the highly complex and unpredictable structures resulting from many natural phenomena, using self-similarity property. The most common mathematical method to generate self-similar fractals is using an iterated function system (IFS). This paper discusses separation properties of finite products of hyperbolic IFSs. Characterizations for totally disconnected and overlapping product IFSs are obtained. A method to generate an open set which satisfies the open set condition for a totally disconnected IFS is given. Some necessary and sufficient conditions for a product IFS to be just touching are discussed. Also, Type 1 homogenous IFSs are introduced and its separation properties in terms of the separation properties of coordinate projections are explained towards the end. (C) 2018 Elsevier B.V. All rights reserved.
Authors
I am an author on this paper
Click your name to claim this paper and add it to your profile.
Reviews
Recommended
No Data Available