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Issue No.03 - May/June (1994 vol.14)
pp: 73-82
ABSTRACT
<p>The presented algorithm generates approximations of self-similar fractal sets. The algorithm is based on a pattern rewriting system that draws a geometric pattern repeatedly after suitable mappings. A program developed from the algorithm reproduces Mandelbrot's self-similar fractals. We begin by discussing fractals and dimension theory, then present the algorithm, and conclude by using fractal set theory to calculate the dimensions of self-similar sets from their generators.</p>
CITATION
Stephen D. Casey, "Self-Similar Fractal Sets: Theory and Procedure", IEEE Computer Graphics and Applications, vol.14, no. 3, pp. 73-82, May/June 1994, doi:10.1109/38.279048
REFERENCES
1. B.B. Mandelbrot,The Fractal Geometry of Nature, W. H. Freeman, New York, 1983.
2. J.R. Munkres,Topology: A First Course, Prentice-Hall, Englewood Cliffs, N.J., 1975.
3. J.E. Hutchinson, "Fractals and Self-Similarity,"Indiana Univ. Mathematics J., Vol. 30, 1981, pp. 713-747.
4. M.F. Barnsley,Fractals Everywhere, Academic Press, Boston, 1988.
5. S.D. Casey, "Analysis of Fractal and Pareto-Levy Sets: Theory and Application,"Proc. European Frequency and Time Forum, Neuchâtel, Switzerland, 1990, pp. 205-211.
6. S. J. Taylor, "The Measure Theory of Random Fractals,"Mathematical Proc. Cambridge Philosophical Soc., Vol. 100, No. 383, 1986, pp. 383-406.
7. B. West,An Essay on the Importance of Being Nonlinear, Springer-Verlag, Berlin, 1985.
8. W. Hurewicz and H. Wallman,Dimension Theory, Princeton Univ. Press, Princeton, N.J., 1941.
9. K. Falconer,The Geometry of Fractal Sets, Cambridge Univ. Press, Cambridge, 1985.
10. K. Falconer,Fractal Geometry: Mathematical Foundations and Applications, John Wiley and Sons, Chichester, England, 1990.
11. H. Federer,Geometric Measure Theory, Springer-Verlag, New York, 1969.
12. H.-O. Peitgen and D. Saupe,The Science of Fractal Images, Springer-Verlag, New York, 1988.
13. H. Abelson and A.A. diSessa,Turtle Geometry, MIT Press, Cambridge, Mass., 1980.
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