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 ?
Estimating the fractal dimension of synthetic topographic surfaces.
DETERMINATION OF FRACTAL DIMENSION FOR SOUTHEAST MISSOURI REGION SEISMIC ZONE.
This seemingly paradoxical situation can be explained by applying the model of pragmatic information to backward causation and introducing a fractal dimension of time.
The fractal dimension comprised Euclidean and non-Euclidean component.
Higuchi fractal dimension (HFD) measures the complexity and self-similarity of a signal [1, 12] in the time domain.
Within our fractal model [1] of matter as a chain system of oscillating protons and under the consideration of quantum oscillations as model mechanism of mass generation [9], we interpret the exponent D in (1) as a Hausdorff [12] fractal dimension of similarity (2):
In this study, we estimate the fractal dimension of price returns and test the Efficient Market Hypothesis (EMH), employing rescaled range analysis in order to use fewer assumptions about the underlying system.
By assuming that the root system resembles a fractal-like structure, we used a technique termed the "box counting method" to calculate the fractal dimension (a number between 1 and 2 for two-dimensional images) of the root images.
The topics include effective properties of heterogeneous magneto-electro-elastic materials with multi-coated inclusions, analyzing the transient hygrothermal aging of hybrid composite materials in asymmetric environments, the influence of the fractal dimension on the mechanical properties of granular materials, validating mechanical damage monitoring on aluminum freestanding thin films using electrical measurements, and investigating the mechanical properties of single-walled carbon nanotubes using the finite element method.
In analyzing United States-Mexican Relations, I employ the mathematical concept of Fractal Dimension and Complexity Theory to explore the idea of spectrum progressing from more orderly to less orderly or to pure disorder in the text, since other works on the topic had characterized Mexico as having been extremely chaotic and backward (more on this later).