Related papers: Fractal Texture and Structure of Central Place Sys…
This study proposes a method for producing an infinite number of fractals using aperiodic substitution tilings, exemplified by the Ammann Chair tiling. Higher-order substitutions of aperiodic tilings are utilized in relation to the…
In this work, we present a mathematical model to describe the adsorption-diffusion process on fractal porous materials. This model is based on the fractal continuum approach and considers the scale-invariant properties of the surface and…
This work proposes a novel technique for the numerical calculus of the fractal dimension of fractal objects which can be represented as a closed contour. The proposed method maps the fractal contour onto a complex signal and calculates its…
This paper presents a versatile model for generating fractal complex networks that closely mirror the properties of real-world systems. By combining features of reverse renormalization and evolving network models, the proposed approach…
There are various notions of dimension in fractal geometry to characterise (random and non-random) subsets of $\mathbb R^d$. In this expository text, we discuss their analogues for infinite subsets of $\mathbb Z^d$ and, more generally, for…
The concept of derivative coordinate functions proved useful in the formulation of analytic fractal functions to represent smooth symmetric binary fractal trees [1]. In this paper we introduce a new geometry that defines the fractal space…
Understanding the intricate architecture of brain networks and its connection to brain function is essential for deciphering the underlying principles of cognition and disease. While traditional graph-theoretical measures have been widely…
One of the most important tasks in image processing problem and machine vision is object recognition, and the success of many proposed methods relies on a suitable choice of algorithm for the segmentation of an image. This paper focuses on…
City size distributions are known to be well approximated by power laws across a wide range of countries. But such distributions are also meaningful at other spatial scales, such as within certain regions of a country. Using data from…
We introduce fractional flat space, described by a continuous geometry with constant non-integer Hausdorff and spectral dimensions. This is the analogue of Euclidean space, but with anomalous scaling and diffusion properties. The basic tool…
Fractal structures appear in a vast range of physical systems. A literature survey including all experimental papers on fractals which appeared in the six Physical Review journals (A-E and Letters) during the 1990's shows that experimental…
Assuming a fractal distribution of matter in the universe, consequences that follow from the General Theory of Relativity and the Copernican Principle for fractal cosmology are examined. The change in perspective necessary to deal with a…
The fracture characterization using a geostatistical tool with conditioning data is a computationally efficient tool for subsurface flow and transport applications. The main objective of the paper is to propose a framework of geostatistical…
We establish a correspondence between Pavlovian conditioning processes and fractals. The association strength at a training trial corresponds to a point in a disconnected set at a given iteration level. In this way, one can represent a…
We propose a novel stochastic network model, called Fractal Gaussian Network (FGN), that embodies well-defined and analytically tractable fractal structures. Such fractal structures have been empirically observed in diverse applications.…
According to some recent analysis (M. Baiesi and M. Paczuski, Phys. Rev. E {\bf 69}, 066106, 2004 \cite{maya1}) of earthquake data, aftershock epicenters can be considered to represent the nodes of a network where the linking scheme depends…
Analysis and modeling of networked objects are fundamental pieces of modern data mining. Most real-world networks, from biological to social ones, are known to have common structural properties. These properties allow us to model the growth…
The theory of resource distribution in self-organizing systems on the basis of the fractal-cluster method has been presented. In turn, the fractal-cluster method is based on the fractal-cluster relations of V.P. Burdakov and the analytical…
In this paper, we present high-level overviews of tile-based self-assembling systems capable of producing complex, infinite, aperiodic structures known as discrete self-similar fractals. Fractals have a variety of interesting mathematical…
Fractal structures naturally emerge in quantum systems whose initial states exhibit spatial discontinuities, a phenomenon first identified by Berry in the paradigmatic case of a particle confined in an infinite potential well. While…