Related papers: Fractal Texture and Structure of Central Place Sys…
We present a formalism that leads very naturally to a hierarchical description of the different contrast structures in images, providing precise definitions of sharp edges and other texture components. Within this formalism, we achieve a…
Most of the known methods for estimating the fractal dimension of fractal sets are based on the evaluation of a single geometric characteristic, e.g. the volume of its parallel sets. We propose a method involving the evaluation of several…
We introduce a fractal version of the pinwheel substitution tiling. There are thirteen basic prototiles, all of which have fractal boundaries. These tiles, along with their reflections and rotations, create a tiling space which is mutually…
Fractals emerge everywhere in nature, exhibiting intricate geometric complexities through the self-organizing patterns that span across multiple scales. Here, we investigate beyond steady-states the interplay between this geometry and the…
This paper focuses on the challenge of interactively modeling street networks. In this work, we extend the simple fractal model, which is particularly useful for describing small cities or individual districts, by constructing random cities…
This is a brief introduction to fractals, multifractals and wavelets in an accessible way, in order that the founding ideas of those strange and intriguing newcomers to science as fractals may be communicated to a wider public. Fractals are…
To remove the confusion of concepts about different sorts of geographical space and dimension, a new framework of space theory is proposed in this paper. Based on three sets of fractal dimensions, the geographical space is divided into…
The cosmic web is one of the most complex systems in nature, consisting of galaxies and clusters of galaxies joined by filaments and walls, leaving large empty regions called cosmic voids. The most common method of describing the web is a…
Fractal dimension is defined on the base of entropy, including macro state entropy and information entropy. The generalized correlation dimension of multifractals is based on Renyi entropy. However, the mathematical transform from entropy…
The effect of geometry and morphology of superconducting structure on magnetic flux trapping is considered. It is found that the clusters of normal phase, which act as pinning centers, have significant fractal properties. The fractal…
A model for the generation of fractal growth networks in Euclidean spaces of arbitrary dimension is presented. These networks are considered as the spatial support of reaction-diffusion and pattern formation processes. The local dynamics at…
In the interstellar medium, as well as in the Universe, large density fluctuations are observed, that obey power-law density distributions and correlation functions. These structures are hierarchical, chaotic, turbulent, but are also…
Fractal dimension constitutes the main tool to test for fractal patterns in Euclidean contexts. For this purpose, it is always used the box dimension, since it is easy to calculate, though the Hausdorff dimension, which is the oldest and…
The fractal dimension curves of urban form and growth fall into two categories: One can be described by common logistic function, and the other can be described with quadratic logistic function. The approach to estimating the parameter of…
Clouds in observations are fractals: they show self-similarity across scales ranging from one to 1000 km. This includes individual storms and large-scale cloud structures typical of organised convection. It is not known whether global…
Fractal geometry, defined by self-similar patterns across scales, is crucial for understanding natural structures. This work addresses the fractal inverse problem, which involves extracting fractal codes from images to explain these…
We show that fractality in complex networks arises from the geometric self-similarity of their built-in hierarchical community-like structure, which is mathematically described by the scale-invariant equation for the masses of the boxes…
The evolution and spatial structure of displacement fronts in fractures with self-affine rough walls are studied by numerical simulations. The fractures are open and the two faces are identical but shifted along their mean plane, either…
Fractals are geometric shapes that can display complex and self-similar patterns found in nature (e.g., clouds and plants). Recent works in visual recognition have leveraged this property to create random fractal images for model…
The fractal structure of directed percolation clusters, grown at the percolation threshold inside parabolic-like systems, is studied in two dimensions via Monte Carlo simulations. With a free surface at y=\pm Cx^k and a dynamical exponent…