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
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  of matter as a chain system of oscillating protons and under the consideration of quantum oscillations as model mechanism of mass generation , we interpret the exponent D in (1) as a Hausdorff  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.
The HFD algorithm calculates fractal dimension
of time series directly in the time domain .
The contours with the maximum fractal dimension
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).