The fractals theory is also closely linked to the chaos theory.
With fractals the rules are precise and the result is predictable.
Besides pore structure analysis, fractal theory has also been used to predict porous media permeability [23, 24].
According to fractal geometry theory, when pore structures are fractal, the relationship between the pore number and pore radius can be presented as 
Li, "Some fractal characters of porous media," Fractals, vol.
However, fractal theory has been found to be an effective method for characterizing complex porous media; for example, it can be used for pore structure identification, diffusion coefficient, permeability coefficient measurement, and so on [2-5].
A detailed analysis of thermofractals and their properties allows one to show that the density in (1) can be written in terms of F and E for a fractal at an arbitrary level n as
Notice that for a fixed value of the scale M, at a fixed level n of the fractal structure, the equation above is a well-defined continuous function and a simple analysis would lead one to conclude that dimension D is not fractal but reflects the topology of the phase-space where the system is embedded.
The first goal of this study is to measure the sprawl and complexity of the adjacent administrative districts of Atakum, Ilkadim and Canik in Samsun, Turkey in the years 1989, 2000 and 2013, during which these districts experienced rapid growth, using Shannon's entropy and fractal analysis based on remote sensing and GIS.
Shannon's entropy was used to measure the urban sprawl, and fractal analysis was used to identify the sprawl characteristics.
Regarding the modeling of the 3D rough fractal
surface, we introduce here a bandlimited Weierstrass function of two variables, (1) below, as a straightforward extension of similar Weierstrass functions provided in the past by Jaggard  (function of one variable) and by Zaleski  (function of two variables).
On the basis of Biot-Allard model and the proposed static flow resistivity formula, a fractal
acoustic model was presented to investigate the acoustic performance of the PFMM.