However, for a better performance of economic and financial forecasts, predictions and the impact of decisions throughout the economy, we argue that fractals pattern are more than helpful be taken into account, fractals can let financial experts to be aware or prepared for periods of cyclical recession and take better and less risky business decisions.
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Then fractal dimension [D.sub.f] can be calculated from the lg [S.sub.Hg]-lg [p.sub.c] plot.
Method I reflects the fractal characteristics of the capillary tube distribution in the cross-section of core samples, which is in two-dimensional space, and the range of the calculated fractal dimension using method I is 1 < [D.sub.f] < 2.
In fractal geometry, the fractal dimension is the objective tool used to measure the degree of "irregularity" and "complexity" in two fractal sets.
where [phi] is porosity, De is the Euclidean space dimension, and [D.sub.f] is the fractal dimension.
The fractal dimension D was determined in terms of the parameters that characterize thermofractals  and is given by
Equation (9) represents the fundamental properties of the fractal structure under scale transformation.
The notion of "fractal" was introduced by Mandelbrot (1983) and comes from the Latin term "fractus", meaning irregular and fragmented; this term is a general expression for self-similarity (Hirata et al.
Fractal objects develop via the repetition of the same principles from small scales to large scales.
where [sigma] is the standard deviation (rms height), C is the amplitude control factor, N is the number of tones, [b.sub.1] and [b.sub.2] ([b.sub.1] > 1, [b.sub.2] > 1) are the spatial-frequency scaling parameters, b is a constant (b > 1), D (2 < D < 3) is the roughness fractal
dimension, [K.sub.1] and [K.sub.2] are the fundamental spatial wave numbers in the direction of x and y respectively, and [[phi].sub.n1], [[phi].sub.n2] are arbitrary phases with uniform distribution over the interval [-[pi], [pi]].
where M([epsilon]) means the length of a line, the area of a surface, the volume of a cube, or the weight of an object; D is the fractal