# Fractal Distribution

## Fractal Distribution

A probability density function that is statistically self-similar. That is, in different increments of time, the statistical characteristics remain the same.
References in periodicals archive ?
A study of four bituminous coals and oxidized bituminous coal samples at 270[degrees]C was able to determine the fractal dimensions and fractal distribution sensitivities to oxidation treatments [9].
Zhao, "Fractal distribution for rock mass in fractures for rock mass in high slopes and its application to the lock of three gorges," Chinese Journal of Geotechnical Engineering, vol.
The property of offering a fractal distribution of responses to a series of fixed stimuli results from the control structure in question being located at an instability; the locus of control is an instability, a condition that is not difficult to arrange, since critical instabilities occur naturally in cybernetic control systems, as Norbert Wiener who formulated their theory in his book, Cybernetics, was first to point out (Wiener, 1948).
If data possess fractal distribution, then double logarithmic diagram of the t and s show linear trend and have slope H (Fig.
Thomas Sieverst's vision upon urban sprawl reality is expounded through a fractal distribution of the elements located at the limit between the city and the surrounding agricultural/rural areas.
Equation (16) is the expression for fractal distribution of pore during the breaking process of coal body.
It was proposed that smoothing of microscopic characteristics over the physically infinitesimal volume transforms the initial fractal distribution into fractional continuous model that uses fractional integrals [15].
This however, was here found empirically, to the best of our knowledge there is no way to calculate directly which nominator reproduces best the fractal distribution. It must still be done by trial and error combined with intuition.
The topology that emerges on the web will depend on the individual choices of many people, but in accordance with previous studies of web usage, we believe it will be a fractal distribution, emphasizing all scales.
The results show that the precipitation series fit a fractal distribution. Values of lie in the range 1.1886-1.5903 with a mean of D= 1.32652 [+ or -] 0.0395, in accordance with those obtained in previous studies.
In the dual porosity, the original channel diameter of embedded fractal-like tree networks follows a fractal distribution. A percolation term ([rho]' - [[rho]'.sub.c]) was obtained using a series of geometric properties of fracture networks and had a high correlation coefficient between the actual and the predicted equivalent fracture network permeability.

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