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International Conference on Complex Systems (ICCS2006)

Reduction of fractal structures to regular one

Ihar Miklashevich
Belarusian national technical university

Ninel Sokolova
Balarusian National Technical University

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     Last modified: May 12, 2006

Abstract
The fractal properties of some of natural processes are well known today. Some times the mathematical representation of this properties is very developed but the physical background of this processes not very clear. The main philosophical problem consist in transition between internal space of state real objects which is smooth manifolds to the fractal representatin. In what stage the fractality is arisen?

Follow to physical interpretation the method to determine the fractal dimension of any surface is proposed. The method based on the multidimensional Pythagorean theorem and deformation of the scales in fractal space. Follow the special space stretching procedure we can transform the fractal consequense to the regular one. In this stretched space relation of two fractal values is the non-fractal. The upper and lower limits of fractal length is found. It is shown that set of fractal squares is unlimited.




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