IJPAM: Volume 70, No. 3 (2011)

THE GRAPH OF FRACTAL DIMENSIONS OF JULIA SETS

Bünyamin Demir$^1$, Yunus Özdemir$^2$, Mustafa Saltan$^3$
$^{1,2,3}$Department of Mathematics
Anadolu University
Eskişehir, TURKEY


Abstract. We obtain Julia sets of $f_c(z)=z^2+c$ using modified inverse iteration method for all c in some grid of the square $[-2,2]\times [-2,2]$ and compute fractal dimensions of them. Then we give the whole picture by drawing the graph of fractal dimensions of Julia sets which resembles the Mandelbrot set.

Received: March 17, 2011

AMS Subject Classification: 26A18, 30D05

Key Words and Phrases: modified inverse iteration method, Julia set, fractal dimension

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Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2011
Volume: 70
Issue: 3