FRACTAL DIMENSION CALCULATING OF REGULAR FRACTALS BY FRAUNHOFER DIFFRACTION

Zinchik Alexander A, Yana Muzychenko, Smirnov Alexander Vitalievich, Stafeev Sergey K.

2009 , VOLUME 09, NUMBER 2 ( MARCH-APRIL )

ISSN 2226-1494 (print), ISSN 2500-0373 (online)

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Vladimir O.
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FRACTAL DIMENSION CALCULATING OF REGULAR FRACTALS BY FRAUNHOFER DIFFRACTION

A. A. Zinchik, Y. Muzychenko, A. V. Smirnov, S. K. Stafeev

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Abstract

The numerical simulation of Fraunhofer diffraction of geometric fractals was made and the original algorithm for calculating the fractal dimension of the regular fractal on the diffraction pattern was suggested. As an example, the diffraction patterns from the following geometrical fractals were used: Sierpinski carpet, Vishek fractal, Koch snowflake. A comparison of the fractal dimension values derived from the numerical experiment with the theoretical values was made. For the generation of fractals with the level m = 6 the difference between these values does not exceed 1.5%.

Keywords: fractal, Fraunhofer diffraction, Fourier transform, fractal dimension, self-similarity, power-law.

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