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 ?
In addition fractal dimensions in geological and mineralogy, lithology, stratigraphy, fluid phases, alteration zones and structural feature [28].
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.
A fractal is a geometric object which is constructed from a "simple" initial shape and arranged to form self-similar patterns across different scales and with fractal dimensions.
He explains how to do the analysis, in chapters on such aspects as a fractal world, from the fractal dimension to multi-fractal spectra, the fractal dimensions of rank-size distributions, geographical explanations of fractal forms and dynamics, and land-use planning and managing a fractal environment.
Fractal model for simulating the space-filling process of cement hydrates and fractal dimensions of pore structure of cement-based materials.
At the same time, the surface fractal dimensions of OS/SC particles by FHH model calculation were obtained.
For example, Lucy Pollard-Gott reveals words or sounds in the poetry of Wallace Stevens that repeat in patterns similar to common fractal dimensions.
We will now present a general method to calculate the fractal dimensions and average colour of the spacetime diagrams of linear CA in [M.
In this first volume of the series Advances in Cognitive Informations and Natural Intelligence, contributors from computing, psychology, and engineering discuss such topics as the theoretical framework of the new discipline, the cognitive process of decision making, adaptive neural networks for trajectory planning, a fixpoint semantics for rule-based anomalies, and a unified approach to fractal dimensions.
The three species (Eastern Wood-Pewee, Eastern Phoebe, and Great Crested Flycatcher) showing positive correlations with fractal dimension appeared to do best in relatively undisturbed areas with comparatively high fractal dimensions.
The fractal dimensions were evaluated for flocs formed under the influence of low (~ 5 ppmv) and high (~ 30 ppmv) concentrations of chemical type F (Figure 9).