Fractal Dimension

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Fractal Dimension

A number that quantitatively describes how an object fills its space. In Euclidean, or Plane geometry, objects are solid and continuous. That is, they have no holes or gaps. As such, they have integer dimensions. Fractals are rough and often discontinuous, like a wiffle ball, and so have fractional, or fractal dimensions.

Fractal Dimension

A description of how a discontinuous object fills the space it occupies. For example, a basketball is not smooth; rather it has lines and grooves all over it. Because it is not a perfect sphere, it requires fractal dimensions to explain how it exists.
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Smooth surfaces are the result of diffusive and depositional processes which result in lowering of fractal dimensions.
GIS-based assessment of surface deformation patterns using fractal analysis of topography: Kharmankuh anticline, Zagros Mountains, Iran
Water treeing can be quantitatively described in terms of the fractal dimension, i.
Relaxations losses in polyethylene insulation of coaxial cable structure during aging in high humidity conditions
Complex, noninteger dimensions are called fractal dimensions [35].
Application of Chaos Theory in the Prediction of Motorised Traffic Flows on Urban Networks
Relations between Fractal Dimensions and Other Notions of Complexity: An Incomplete Survey of the Literature.
Fractal dimension versus process complexity
The fractal dimensions of different sizes of aggregates may have various effects on the high-temperature performance (in regard to high-temperature stability and maximum shear stress).
The effect of morphological characteristic of coarse aggregates measured with fractal dimension on asphalt mixture's high-temperature performance
Jain, "Relationship between diabetes and grayscale fractal dimensions of retinal vasculature in the Indian population," BMC Ophthalmology, vol.
Automatic analysis of retinal vascular parameters for detection of diabetes in indian patients with no retinopathy sign
Many physical processes produce fractal property, and a natural scene can be modeled by fractal dimension [6].
Chaotic features for dynamic textures recognition with group sparsity representation
Their fractal dimensions were computed using box-counting algorithm.
Financial volatility measurement using fractal dimension
From each linear regression D are obtained, which generate an spectrum of generalized fractal dimensions [D.
Bioinformatica multifractal: una propuesta hacia la interpretacion no-lineal del genoma
A multifractal is a set composed of a multitude of interwoven subsets, each of differing fractal dimensions.
Multifractal characterization of unworn hydrogel contact lens surfaces
Extracted ROIs in both LUMISYS and HOWTEK volumes were analyzed by fractal algorithm, their corresponding fractal dimensions are calculated.
Fractal dimension based detection of architectural distortion anomalies in mammography
Landini G, Rippin JW Fractal dimensions of the epithelial-connective tissue interfaces in premalignant and malignant epithelial lesions of the floor of the mouth.
Fractal and Euclidean geometric diagnostic methodology of uterine cervix cells/Metodologia diagnostica geometrica fractal y euclidiana de celulas del cuello uterino

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