Circle Inversion Fractals

B. Boreland () and H. Kunze ()
Additional contact information
B. Boreland: University of Guelph, Department of Mathematics and Statistics
H. Kunze: University of Guelph, Department of Mathematics and Statistics

A chapter in Mathematical and Computational Approaches in Advancing Modern Science and Engineering, 2016, pp 609-619 from Springer

Abstract: Abstract In 2000, Frame and Cogevina (Comput Graph 24(5):797–804, 2000) introduced a method for constructing fractals using circle inversion maps. The literature (Clancy and Frame, Fractals 3:689–699, 1995; Frame et al., A fractal representation of grammatical complexity in time series. Manuscript in Preparation, 1996; Frame and Cogevina, Comput Graph 24(5):797–804, 2000; Leys, Comput Graph 29(3):463–466, 2005) focuses on the graphical aspect of such fractals, without presenting a careful development of the underlying mathematical framework. In this paper, we present such a framework, making a strong connection to iterated function systems (IFS) theory. Our final result establishes that the set valued system of circle inversion maps induced by a collection of non-touching circles in the plane has a unique set attractor. We present a graphical example using the chaos game.

Keywords: Circle Inversion; Chaos Game; Iterated Function Systems (IFS); Graphical Aspects; Grammatical Complexity (search for similar items in EconPapers)
Date: 2016
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-30379-6_55

Ordering information: This item can be ordered from
http://www.springer.com/9783319303796

DOI: 10.1007/978-3-319-30379-6_55

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().