Serpinsky carpet

The following equation was obtained for exponent r at simulation of fractal structure as Serpinsky carpet [1] ... 

The following equation for the exponent q was obtained at a fractal structure simulation as Serpinsky carpet [75] ... 

According to Family s classification [8], fractal objects can be divided into two main types deterministic and statistical. The deterministic fractals are self-similar objects, which are precisely constructed on the basis of some basic laws. Typical examples of such fractals are the Cantor set ( dust ), the Koch curve, the Serpinski carpet, the Vichek snowflake and so on. The two most important properties of deterministic fractals are the possibility of precise calculation of their fractal dimension and the unlimited range (- o +°°) of their self-similarity. Since a line, plane or volume can be divided into an infinite number of fragments by various modes then it is possible to construct an infinite number of deterministic fractals with different fractal dimensions. In this connection the deterministic fractals are impossible to classify without introduction of their other parameters in addition to the fractal dimension. 

For regular mathematical fractals of Cantor sets, Koch curves and Serpinski carpets, constructed by recurrent procedures, the Renie dimension d does not depend on q, but on [14] ... 

For the exponent q at fractal structure simulation as a Serpinsky carpet the following equation was obtained [21] ... 

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See also in sourсe #XX -- [ , ]

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