Related papers: Drip Paintings and Fractal Analysis
It is wellknown that the ordinary calculus is inadequate to handle fractal structures and processes and another suitable calculus needs to be developed for this purpose. Recently it was realized that fractional calculus with suitable…
The boundaries of central place models proved to be fractal lines, which compose fractal texture of central place networks. A textural fractal can be employed to explain the scale-free property of regional boundaries such as border lines,…
Fractal geometry deals mainly with irregularity and captures the complexity of a structure or phenomenon. In this article, we focus on the approximation of set-valued functions using modern machinery on the subject of fractal geometry. We…
We have built a new kind of manifolds which leads to an alternative new geometrical space. The study of the nowhere differentiable functions via a family of mean functions leads to a new characterization of this category of functions. A…
In this paper, we present an effective method to characterize completely when a disconnected fractal square has only finitely many connected components. Our method is to establish some graph structures on fractal squares to reveal the…
Fractal behaviour, i.e. scale invariance in spatio-temporal dynamics, have been found to describe and model many systems in nature, in particular fluid mechanics and geophysical related geometrical objects, like the convective boundary…
Fractal structures emerge from statistical and hierarchical processes in urban development or network evolution. In a class of efficient and robust geographical networks, we derive the size distribution of layered areas, and estimate the…
Naive scale invariance is not a true property of natural images. Natural monochrome images posses a much richer geometrical structure, that is particularly well described in terms of multiscaling relations. This means that the pixels of a…
The concept of self-similarity on subsets of algebraic varieties is defined by considering algebraic endomorphisms of the variety as `similarity' maps. Self-similar fractals are subsets of algebraic varieties which can be written as a…
In this paper, we prove intractability results about sampling from the set of partitions of a planar graph into connected components. Our proofs are motivated by a technique introduced by Jerrum, Valiant, and Vazirani. Moreover, we use…
Critical systems have always intrigued physicists and precipitated the development of new techniques. Recently, there has been renewed interest in the information contained in their classical configurations, whose computation do not require…
The conventional mathematical methods are based on characteristic length, while urban form has no characteristic length in many aspects. Urban area is a measure of scale dependence, which indicates the scale-free distribution of urban…
The curves of scaling behavior is a significant concept in fractal dimension analysis of complex systems. However, the underlying rationale of this kind of curves for fractal cities is not yet clear. The aim of this paper is at researching…
The light scattering experiment establishes a relationship between refractive index fluctuations and fractal dimension in weakly scattering tissue-like media. Based on the box-counting approach, an analytical model is developed and shows…
We estimate a Box-counting dimension of fractal surfaces which are generated by iterated function systems with a vertical contraction factor function on an arbitrary data set over rectangular grids and can express well a lot of natural…
Geometrical properties of landscapes result from the geological processes that have acted through time. The quantitative analysis of natural relief represents an objective form of aiding in the visual interpretation of landscapes, as…
The science of fractography revolves around the correlation between topographic characteristics of the fracture surface and the mechanisms and external conditions leading to their creation. While being a topic of investigation for…
This work proposes to obtain novel fractal descriptors from gray-level texture images by combining information from interior and boundary measures of the Minkowski dilation applied to the texture surface. At first, the image is converted…
We prove the existence of the reflected diffusion on a complex of an arbitrary size for a large class of planar simple nested fractals. Such a process is obtained as a folding projection of the free Brownian motion from the unbounded…
We simulate a two-dimensional array of droplets being compressed between two walls. The droplets are adhesive due to an attractive depletion force. As one wall moves toward the other, the droplet array is compressed and eventually induced…