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The Effect of Multiple Rotations on Mobius Transformations in Generating IFS Fractals

by T. Gangopadhyay
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International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
Volume 142 - Number 6
Year of Publication: 2016
Authors: T. Gangopadhyay
10.5120/ijca2016909821

T. Gangopadhyay . The Effect of Multiple Rotations on Mobius Transformations in Generating IFS Fractals. International Journal of Computer Applications. 142, 6 ( May 2016), 18-22. DOI=10.5120/ijca2016909821

@article{ 10.5120/ijca2016909821,
author = { T. Gangopadhyay },
title = { The Effect of Multiple Rotations on Mobius Transformations in Generating IFS Fractals },
journal = { International Journal of Computer Applications },
issue_date = { May 2016 },
volume = { 142 },
number = { 6 },
month = { May },
year = { 2016 },
issn = { 0975-8887 },
pages = { 18-22 },
numpages = {9},
url = { https://ijcaonline.org/archives/volume142/number6/24900-2016909821/ },
doi = { 10.5120/ijca2016909821 },
publisher = {Foundation of Computer Science (FCS), NY, USA},
address = {New York, USA}
}
%0 Journal Article
%1 2024-02-06T23:45:06.505811+05:30
%A T. Gangopadhyay
%T The Effect of Multiple Rotations on Mobius Transformations in Generating IFS Fractals
%J International Journal of Computer Applications
%@ 0975-8887
%V 142
%N 6
%P 18-22
%D 2016
%I Foundation of Computer Science (FCS), NY, USA
Abstract

Iterating two pairs of Mobius transformations as attractors generates fractals that are known as Mobius fractals. In the present paper one studies the effect of multiple rotations on Mobius transformations, that frequently lead to more well-rounded as well as original fractal designs.

References
  1. Bourke, P.: An Introduction to the Apollony Fractal. Computers and Graphics, 30( 2006) 134–136.
  2. Gangopadhyay, T. IFS Fractals generated by Affine Transformation with Trigonometric Coefficients and their Transformations, International journal of Computer Applications 53(2012) 29-32..
  3. Gangopadhyay, T. The Effect of Multiple Rotations on a Unified System of Affine Transformations with Related Trigonometric Coefficients, International journal of Computer Applications April(2016)(in press)..
  4. Krantz, S. G. "Möbius Transformations." §6.2.2 in Handbook of Complex Variables. Boston, MA: Birkhäuser, p. 81, 1999..
  5. Benoit B. Mandelbrot, Miroslav Michal Novak, Thinking in Patterns: Fractals and Related Phenomena in Nature
  6. Mumford , D et al. Indra’s Pearls, Cambridge University Press, 2002
  7. Needham, T. "Möbius Transformations and Inversion." Ch. 3 in Visual Complex Analysis. New York: Clarendon Press, pp. 122-188, 2000.html.
  8. Stevens, R. Creating Fractals, Charles River media, Inc. 2005
Index Terms

Computer Science
Information Sciences

Keywords

Mobius IFS rotations .

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