TITLE:
An Analytical Model for Multifractal Systems
AUTHORS:
Jun Li
KEYWORDS:
Multifractal, Jake-Jun Model, Cantor Set, Sierpinski Carpet, Price Oscillation
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.4 No.7,
July
4,
2016
ABSTRACT: Previous multifractal spectrum theories can only reflect that an object is multifractal and few explicit expressions of f(α) can be obtained for the practical application of nonlinearity measure. In this paper, an analytical model for multifractal systems is developed by combining and improving the Jake model, Tyler fractal model and Gompertz curve, which allows one to obtain explicit expressions of a multifractal spectrum. The results show that the model can deal with many classical multifractal examples well, such as soil particle-size distributions, non-standard Sierpinski carpet and three-piece-fractal market price oscillations. Applied to the soil physics, the model can effectively predict the cumulative mass of particles across the entire range of soil textural classes.