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.
References in periodicals archive ?
Nevertheless, the variation becomes complicated when the fractal dimension D is involved.
To illustrate the fractal function of (1) for different values of fractal dimension D, some representative simulations of that are shown in Fig.
Fractal dimension mapping us to ascertain geomorphic domains where variability of fractal dimension of the earth surface represents the roughness of the land form topography and is an assessment of texture of topography.
Feature representation of EGG signals based on fractal dimension
As it can be observed from the Table 1, dead bacteria show higher fractal dimension and smaller roundness as compared to live bacteria.
Using the data, weighted kappas were calculated, and fractal dimension in each image was calculated using the box counting method.
Obviously, in a thermoplastic polyethylene insulation water clusters with similar fractal dimensions are formed.
Furthermore, it can be noted that among the hundred studied roughness parameters, the most relevant of them to discriminate the topography of the overall polypropylene abraded surfaces is the fractal dimension of the profiles.
They include sensitive dependence on initial conditions which are in most cases unknown as most assumptions made often lead to error, the current stage of this "new" discipline of science (just half a century old) as one is not yet very sure of how much data is required to precisely reconstruct phase space and determine the fractal dimension of a given system (discussed in Section 3.
On the one hand, there is a geometrical framework in which the complexity of spatiotemporal objects is measured by their fractal dimension.
The degree of irregularity can be measured by fractal dimension by providing a quantitative index to describe the statistical self-similarity of complex phenomena [10].