Category: Viability, reliability, safety


Smagin V.A. , Bubnov V.P.

A mathematical model for representing deterministic and random processes in the form of a sequence of fractals is proposed. It is based on a information quantization model and a hyperdelta probability distribution. To form a sequence, a nonlinear integral equation with an integer kernel is proposed. It is used to determine basic fractal and subfractals (clusters). An example for uniform distribution is considered. The probabilistic and entropy properties of the decomposition components are evaluated. The influence of the threshold constant in the nonlinear integral equation, which is used to find the value of the base fractal, on its extent is determined. The fractal length is an important characteristic on which the amount of information placed in the fractal on the known law of its distribution depends. The answer to this question is given by examples with two probability distributions. The research results are recommended for use in metrology, information theory and efficiency theory.

Key words:
nonlinear integral equation, basic fractal, constant and its value, graphical and numerical solution, distribution of the amount of information, the length of the fractal

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