Fractals, the theory of fractals are applied at the description of various phenomena, from biological to quantum mechanical. The mathematical model of representation of processes in the form of consecutive hyper fractal distribution is offered. It is based on model of quantization of information and the giperdeltny distribution of probabilities which is earlier offered by the author. For formation of the sequence the nonlinear integrated equation with an integer kernel is offered. On him there are a basic fractal and subfractals (clusters). An example for uniform distribution is reviewed. Estimation of probabilistic and entropy properties of components of decomposition is made. Use in metrology is recommended, to the theory of information and the theory of effi ciency.
the sequences of fractals, subfraktal, the probabilistic properties, entropy properties determined and casual processes
1. Feder J. Fractals. – NY: Springer, 1988. 254 p.
2.
3. Mandelbrot B. B. Les Objets Fractals: Forme, Hasard et Dimension. – Paris: Flammarion, 1975. 190 p.
4.
5. Smagin V. A., Filimonihin G. V. Modelirovanie sluchaynyh processov na osnove giperdel'tnogo raspredeleniya // AVT. 1990. № 5. S. 25-31.
6.
7. Smagin V. A. Korrekciya giperdel'tnogo raspredeleniya v teorii sluchaynyh processov // Intellektual'nye tehnologii na transporte. 2015. № 2. S. 27-31.
8.
9. Smagin V. A. Tehnicheskaya sinergetika. Veroyatnostnye modeli slozhnyh sistem. – SPb., 2004. 171 s.
10.
11. Andronov A. M., Bokoev T. N. Optimal'noe v smysle zapolnenie kvantovanie informacii // Izv. AN SSSR. Tehnicheskaya kibernetika. 1979. № 3. S. 154-158.
12.
13. Dorohov A. N. Metrologicheskoe obespechenie ekspluatacii vooruzheniya i voennoy tehniki: ucheb. / pod red. A. N. Mironova. – SPb., 2009. 755 s.
14.
15. Petuhov G. B. Osnovy teorii effektivnosti celenapravlennyh processov. Ch. 1. Metodologiya, metody, modeli. – SPb., 1989. 660 s.
16.
17. Zaharov A. I., Zagaynov A. I. Realizaciya programmnogo kompleksa dlya vychisleniya fraktal'nyh parametrov slozhnyh sistem // Intellektual'nye tehnologii na transporte. 2015. № 2. S. 47-53.
18.
19. Falconer K. Fractal geometry. – UK: Univ. St. Andrews, 2003. 335 r.
20.
21. Potapov A. A. Fraktaly i drobnye operatory v obrabotke informacii fundamental'noe napravlenie sinergetiki // Izv. YuFU. Tehnicheskie nauki. 2011. № 6. C. 30-40.
22.
23. Li H. Fractal analysis of side channels for breakdown structures in XLPE cable insulation // J. Mater. Sci.: Mater. Electron. Springer Sci. 2013. № 24. R. 1640-1643.
24.
25. Martínez C. A. T., Fuentes C. Chapter 1. Applications of Radial Basis Function Schemes to Fractional Partial Differential Equations // Mathematics Fractal Analysis – Applications in Physics, Engineering and Technology / ed. F. Brambila. 2017.
26.
27. Agboola O., Onyango M. S., Popoola P., Oyewo O. A. Chapter 10. Fractal Geometry and Porosity // Mathematics Fractal Analysis – Applications in Physics, Engineering and Technology / ed. F. Brambila. 2017.