# fractal

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Related to fractal: Fractal dimension
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• noun

## Words related to fractal

### (mathematics) a geometric pattern that is repeated at every scale and so cannot be represented by classical geometry

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Fractals have 'self-similar' structure on a variety of size scales.
Therefore, the equation proposed here, which describes the modified two-dimensional bandlimited fractal Weierstrass function for modeling 3D rough fractal surfaces is given by
Measuring complicated processes of geological phenomena and represent into a single parameter, is one of the advantages of using fractal analysis in the geosciences which would be arduous to measure using just by classic geological approaches (Perugini, and Kueppers, 2012).
Benoit Mandelbrot (1924-2010), often known as the "father of fractal geometry" (Gomory, 2010), revived the study of fractal geometry in the late 1960's, eventually coining the term 'fractal' (stemming from the Latin word for 'broken') in the year 1975.
Moreover, what is palpable is the contrast between the permanent state of the fabric fractals and the unpredictable fractal potentialities of the pigments, in the seemingly restless hands of Wilwayco, who has already proven himself as a master manipulator of oils.
Fractal geometry was introduced by the French mathematician Benoit Mandelbrot, around 1970.
The distance between f and its fractal convolution does not exceed s on the nodes of the partition that is to sayEquation
To find out fractal dimension, linear regression is applied on the whole frequency range to estimate the slope which is linearly related to the fractal dimension of the image.
The number N of boxes of size R needed to cover a fractal set follows a power-law, N = N0 * R^ (-DF), with DF<=D (D is the dimension of the space, usually D = 1, 2, 3), which is repeated with different box sizes.
This paper presents a novel Koch Pentagonal fractal antenna based on iteratively fractalizing pentagonal patch and simultaneously etching the inner sides of the pentagon with Koch fractal antenna of the 1st order for miniaturization and multiband behavior.
As a consequence of their self-similarity and scale invariance properties, many deterministic fractal antennas with geometrical shapes have been reported to fit these requirements [1-6].
Fractal Geometry, closely related to Chaos theory, arose after criticisms of classical Euclidian Geometry.
Fractal theory is a quite active mathematic branch of nonlinear science, and the research objects of which are certain unsmooth or non-differentiable geometries in nonlinear systems and nature.
When eye surgeons would implant the fractal devices in the eyes of blind patients, interface circuitry happens that would collect light captured by the retina and guide it with almost 100 pc efficiency to neurons for relay to the optic nerve to process vision.
The proposed process is based on the elements of the fractal geometry.
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