Fractal

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Related to Fractal curve: fractal dimensionality
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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It is carefully noted that every x(l-j[DELTA]l) represents a point on a m-dimensional fractal curve, where, j = 0, 1, 2, ....
This means that the Euclidean distance is a special case of nonlocal distance whenever the dimension of the fractal curve, m, equals 1.
The proposed novel CSRRs based on Koch fractal curve can be modeled by the equivalent circuit shown in Fig.
Area of the unit cell that uses N CSRR is approximately 36% lower, due to the specific shape of the fractal curve. Furthermore, fractal structure exhibits higher value of the quality factor and higher sharpness of selection than the conventional one.
Circularly arced Koch fractal curve (CAKC) is originally proposed.
All well-known fractal curves, such as Koch curve [13], Peano curve [22], Giuseppe Peano curve [17], and Hilbert Curve [23, 24], are preferably designed into dipole or monopole antennas.
Considering the dynamics of complex system entities that take place on fractal curves, we show that the control of different behaviours of these systems implies nondifferentiability.
(iii) There is infinity of fractal curves (geodesics) relating to any couple of points (or starting from any point) and applied for any scale.
In this paper, square Sierpinski fractal curve is adopted to form the split-ring resonator.
The fractal curves have been known since the end of 19th century, when Peano constructed a continuous curve that passes through every point of a given region.
According to the definition of box dimension of fractal geometry [8] and the formulas above, we can derive fractal dimension of the Kochlike fractal curve along the lateral sides and base side of the isosceles triangle as follows:
We transform rectilinear sides of Sierpinski Gasket into Koch-like fractal curves then we obtain Koch-like sided Sierpinski Gasket multifractal.