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The Effect of Multiple Rotations on a Unified System of Affine Transformations with related Trigonometric Coefficients

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International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
Year of Publication: 2016
Authors:
T. Gangopadhyay
10.5120/ijca2016909114

T Gangopadhyay. Article: The Effect of Multiple Rotations on a Unified System of Affine Transformations with related Trigonometric Coefficients. International Journal of Computer Applications 139(2):30-35, April 2016. Published by Foundation of Computer Science (FCS), NY, USA. BibTeX

@article{key:article,
	author = {T. Gangopadhyay},
	title = {Article: The Effect of Multiple Rotations on a Unified System of Affine Transformations with related Trigonometric Coefficients},
	journal = {International Journal of Computer Applications},
	year = {2016},
	volume = {139},
	number = {2},
	pages = {30-35},
	month = {April},
	note = {Published by Foundation of Computer Science (FCS), NY, USA}
}

Abstract

In IFS fractals generated by affine transformations with arbitrary coefficients often there is a lot of chaotic noise. In the present paper the author studies the effect of multiple rotations on affine transformations with related trigonometric coefficients in terms of the IFS fractals generated by them. In the process a unified set of equations for generating both the Highway Dragon and the C curve have been developed. The effect of multiple rotations is to lend additional depth to the generated fractal as well as create new fractal designs..

References

  1. Barnsley, M. 1983 Fractals Everywhere, Academic Press.
  2. Bulaevsky, J. “The Dragon Curve or Jurassic Park fractal, http://ejad.best.vwh.net/java/fractals/jurasic.shtml.
  3. Gangopadhyay, T. 2012 On generating skyscapes through escape-time fractals, International journal of Computer Applications 43(2012)17-19.
  4. Gangopadhyay, T. 2012 IFS Fractals generated by affine transformation with trigonometric coefficients and their transformations, International journal of Computer Applications 53(2012)29-32,.
  5. Gardner, M. Mathematical Magic Show: More Puzzles, Games, Diversions, Illusions and Other Mathematical Sleight-of-Mind from Scientific American. New York: Vintage, pp. 207-209 and 215-220, 1978.
  6. Paul Lévy, Plane or Space Curves and Surfaces Consisting of Parts Similar to the Whole (1938), reprinted in Classics on Fractals Gerald A. Edgar ed. (1993) Addison-Wesley Publishing ISBN 0-201-58701-7.
  7. Perlin, K. ‘Coherent noise function’, original source code, http://mrl.nyu.edu/~perlin/doc/oscar.html#noise.

Keywords

affine, IFS, rotation, trigonometric.