Fractal


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Related to Fractal: Fractal dimension
A fragmented geometric shape that can be split into parts, each of which approximates a reduced-size copy of the whole, a property which is called self-similarity. Fractals provide the mathematics behind structures in the natural universe—e.g., frost crystals, coastlines, etc.—which cannot be described by the language of euclidean geometry. Fractal analysis is providing new ways to interpret biomedical phenomena. It has been used for classifying histopathology, enzymology, and signal and image compression
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The Authors focused on the comparison between the original fractal approach and the Gaussian one, based on the so-called Gaussian bell.
A fractal is a geometric object that repeats itself in the same structure on different scales and/or timings, showing repeating patterns.
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.
Based on the geometry fractal characteristics of coals, Friesen and Mikula [29] proposed an equation to calculate fractal dimension which can be expressed as
Substituting (4) and (11) into (9), damage variable expression with fractal characteristics can be described as
This figure also demonstrates the return loss for the fractal tree-shaped MSA, which keeps keen for the half year with NaCl fusion, which demonstrates the multiband result overall converted into single band output.
The fractal dimension D was determined in terms of the parameters that characterize thermofractals [20] and is given by
In this paper, the main objective of our research is to offer a new fractal model of normal contact stiffness which is more universal than before.
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.
Figure 3 gives representative examples of scattering patterns from 3D fractal surfaces for different values of fractal dimension D, as numerically calculated by our research group by using (3)-(8) above.
The scaling relationship of the length L and the tortuosity fractal dimension [D.sub.t] by using the formula [mathematical expression not reproducible] was given by Wheatcraft and Tyler [25], where e is the length scale of measurement.