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.
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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.
Since the statistical behaviour of seismicity may potentially represent sensitive short-term predictors of major earthquakes, this study's main aim was to find an empirical relationship between seismic b-values and the fractal distribution of epicentres for Turkish earthquakes.
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].
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.
Their superior fractal distribution and SMB technology further enhances BlueFire's robust and efficient conversion process by efficiently separating the acid and sugar streams.
This process utilizes a patented fractal distribution system in a packed bed countercurrent ion exchange system that results in a near perfect plug flow regime and exceptional separation of waste fractions during the regeneration cycle.
It is important to bear in mind, while utilizing this view of time-series analysis, that fractal distributions are additive; that is, increments of time have individual transactions embedded in them.
Four different fractal distributions of the substrate layers are shown in Figure 3.