Related papers: Fractal Texture and Structure of Central Place Sys…
We investigate the ability of a local bi-orthogonal decomposition to build texture segmentation of images. Using the structures associated to the local decomposition of the image independent row and columns we perform a segmentation, where…
We describe the fractal solid by a special continuous medium model. We propose to describe the fractal solid by a fractional continuous model, where all characteristics and fields are defined everywhere in the volume but they follow some…
Texture plays an important role in computer vision. It is one of the most important visual attributes used in image analysis, once it provides information about pixel organization at different regions of the image. This paper presents a…
A substantial share of the Earth's land surface is managed by humans, with cities representing the most extreme form of anthropogenic land use. There are zillion ways in which settlements can be arranged across a given area, and their…
In many low-dimensional dynamical systems transport coefficients are very irregular, perhaps even fractal functions of control parameters. To analyse this phenomenon we study a dynamical system defined by a piece-wise linear map and…
We proposed a new universal method for significantly increasing accuracy of critical points of 2 and 3-dimensional Ising models and exploring fluctuation mechanism. The method is based on analysis of block fractals and the renormalization…
We propose a mapping from fracture systems consisting of intersecting fracture sheets in three dimensions to an abstract network consisting of nodes and links. This makes it possible to analyze fracture systems with the methods developed…
The fractal properties of models of randomly placed $n$-dimensional spheres ($n$=1,2,3) are studied using standard techniques for calculating fractal dimensions in empirical data (the box counting and Minkowski-sausage techniques). Using…
Our first experience of dimension typically comes in the intuitive Euclidean sense: a line is one dimensional, a plane is two-dimensional, and a volume is three-dimensional. However, following the work of Mandelbrot \cite{mandelbrot},…
We consider the general character of the spatial distribution of a population that grows through reproduction and subsequent local resettlement of new population members. We present several simple one and two-dimensional point placement…
Predicting urban growth is important for practical reasons, and also for the challenge it presents to theoretical frameworks for cluster dynamics. Recently, the model of diffusion limited aggregation (DLA) has been applied to describe urban…
Fracture is a fundamental mechanism of materials failure. Propagating cracks can exhibit a rich dynamical behavior controlled by a subtle interplay between microscopic failure processes in the crack tip region and macroscopic elasticity. We…
A numerical study of the transfer across random fractal surfaces shows that their responses are very close to the response of deterministic model geometries with the same fractal dimension. The simulations of several interfaces with…
Since the recent dissertation by Steffen Winter, for certain self-similar sets $F$ the growth behaviour of the Minkowski functionals of the parallel sets $F_\varepsilon := \{x\in \mathbb R^d : d(x,F)\leq \varepsilon\}$ as $\varepsilon…
We establish pointwise and distributional fractal tube formulas for a large class of relative fractal drums in Euclidean spaces of arbitrary dimensions. A relative fractal drum (or RFD, in short) is an ordered pair $(A,\Omega)$ of subsets…
Algorithmic fractal dimensions -- constructs of computability theory -- have recently been used to answer open questions in classical geometric measure theory, questions of mathematical analysis whose statements do not involve computability…
We present a general theory of fractal transformations and show how it leads to a new type of method for filtering and transforming digital images. This work substantially generalizes earlier work on fractal tops. The approach involves…
We survey recent developments in fractal analysis of regular and slow-fast dynamical systems using Minkowski dimension. Our focus is on spiral trajectories near monodromic limit periodic sets in regular systems and entry-exit sequences in…
The foundation of the theory presented here has already been proved to be effective for the case of curves belonging to the Koch family. The present paper extends the investigation to more complex curves, namely randomly generated curves…
Dynamical zeta functions provide a powerful method to analyze low dimensional dynamical systems when the underlying symbolic dynamics is under control. On the other hand even simple one dimensional maps can show an intricate structure of…