# 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.
Water treeing can be quantitatively described in terms of the fractal dimension, i.
Complex, noninteger dimensions are called fractal dimensions [35].
Relations between Fractal Dimensions and Other Notions of Complexity: An Incomplete Survey of the Literature.
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).
Jain, "Relationship between diabetes and grayscale fractal dimensions of retinal vasculature in the Indian population," BMC Ophthalmology, vol.
Many physical processes produce fractal property, and a natural scene can be modeled by fractal dimension [6].
Their fractal dimensions were computed using box-counting algorithm.
From each linear regression D are obtained, which generate an spectrum of generalized fractal dimensions [D.
A multifractal is a set composed of a multitude of interwoven subsets, each of differing fractal dimensions.
Extracted ROIs in both LUMISYS and HOWTEK volumes were analyzed by fractal algorithm, their corresponding fractal dimensions are calculated.
Landini G, Rippin JW Fractal dimensions of the epithelial-connective tissue interfaces in premalignant and malignant epithelial lesions of the floor of the mouth.

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