Open Access Open Access  Restricted Access Subscription or Fee Access

A Survey on Fractals

S. Sukumaran, Dr. M. Punithavalli

Abstract


Fractal is an irregular and fragmented geometric shape that can be subdivided in parts, where each part appears to be the same in all range of scale. Fractal geometry and its concepts have become central tools in most of the natural sciences. Fractals are of interest to graphic designers and film makers for their ability to create new and exiting shapes and artificial but realistic worlds. Fractals may appear complex, but they can be developed by simple rules.Computer graphics has played an important role in the development and acceptance of fractal geometry. The generation of each fractal is dependent on the approach and algorithm used. Thus it is important to understand the properties of each type of fractals as this will influence the procedure during the generation of fractal. Fractal plays a central role in the realistic rendering and modeling natural phenomena in computer graphics. This paper discusses on the evolution, classification and application of fractals. It also demonstrates the methods to generate the fractals.


Keywords


fractal, fractal dimension, Mandel set, Julia set, self similarity.

Full Text:

PDF

References


A.P. Pentland, Fractal-based description of natural scenes, IEEE Trans.on Pattern Analysis and Machine Intelligence, vol.6, pp 661-674, 1984.

Alice Kelley, Layering techniques in fractal art, Computer and Graphics,vol. 24, pp 611-616, 2000.

Bernt Wahl, Peter Van Roy, Michael Larsen, and Eric Kampman,Exploring Fractals, Addison Wesley, 1995.

Briggs, John. Fractals: The Patterns of Chaos. Thames and Hudson.

Davidoff.K.Fran, Dynamic Fractals, Computer and Graphics, vol.14,no.1 pp 135-136, 1990.

Drakopoulos V. Comparing rendering methods for Julia sets. Journal of WSCG; pp 155–161, 2002.

Entiwistle. D. Ian, Julia set art and Fractals in the complex plane,Computer and Graphics, vol.13, No.3, pp 389-392,1989.

Falconer, Kenneth, Fractal Geometry: Mathematical Foundations and Applications, John Wiley & Sons, 2003.

Falconer, Kenneth, Techniques in Fractal Geometry, John Wiley and Sons, 1997.

Gomatarn J, et al. Generalization of the Mandelbrot set: quaternionic quadratic maps, Chaos, Solitons and Fractals pp. 971–985, 1995.

Hohlfeld. R and Cohen N, Self-Similarity and the Geometric Requirements for Frequency Independence in Antennae, Fractals,vol. 7, No. 1, pp. 79-84, 1999.

J.E.Hutchinson, Fractals and Self-Similarity, Indiana. Univ. Math. J.,1981.

M. A. Arbeiter, Random Recursive Constructions of Self-Similar Fractal Measures, Probability Theory Related Fields, 1991.

M.F.Barnsley, Fractals Everywhere, Academic Press, New York, 1988.

Mandelbrot, B.B. The Fractal Geometry of Nature, W.H.Freeman and Company, 1982.

Peitgen H.O. Saupe D, The Science of Fractal images, Springer, NewYork, 1988.

Peitgen H-O, Richter P.H, The beauty of fractals, Springer, New York,1986.

Peng, Gongwen Decheng Tian, The fractal nature of a fracture surface,Journal of Physics, 1990.

Pickover C, Chaos in wonderland, St. Martin’s Press, 1994.

Pickover C, Keys to infinity, John Wiley and Sons, 1995.

Rankinson R. John, Computer Graphics Software Construction, 1988.

Raul Rojas, A tutorial on efficient computer graphic representations of the Mandelbrot set, Computer and Graphics, vol. 15, No.1, pp, 91-100,1991.

Robert L.Devaney, “Chaos Rules”, Research Article, Sep 2003.

Rochon D, A generalized Mandelbrot set for bicomplex numbers.Fractals, pp. 355–368, 2000.

Ron Eglash, African Fractals: Modern Computing and Indigenous Design, New Brunswick, Rutgers University Press, 1999.


Refbacks

  • There are currently no refbacks.


Creative Commons License
This work is licensed under a Creative Commons Attribution 3.0 License.