Related papers: Fractal Dimension of the Cantor Moire Structures
We establish properties of a new type of fractal which has partial self similarity at all scales. For any collection of iterated functions systems with an associated probability distribution and any positive integer V there is a…
We develop an effective model to describe the dynamics of a system of particle moving in circular configurations around a central mass, by considering the continuum limit of the angular distribution, to obtain the stable configurations for…
The interstellar medium is structured as a hierachy of gas clouds, that looks self-similar over 6 orders of magnitude in scales and 9 in masses. This is one of the more extended fractal in the Universe. At even larger scales, the ensemble…
We prove that the martingale dimensions for canonical diffusion processes on a class of self-similar sets including nested fractals are always one. This provides an affirmative answer to the conjecture of S. Kusuoka [Publ. Res. Inst. Math.…
We analyze the fragmentation behavior of random clusters on the lattice under a process where bonds between neighboring sites are successively broken. Modeling such structures by configurations of a generalized Potts or random-cluster model…
This papers briefly reviews the progress in studying the long-lived filamentary structures of a skeletal form (namely, tubules and cartwheels, and their simple combinations) in electric discharges in various fusion devices. These include…
In this paper two zero-dimensional compact sets with equal topological and fractal dimensions but embedded in Euclidean space by different ways are under study. Diffraction of plane electromagnetic wave propagated and reflected by fractal…
Many natural systems show emergent phenomena at different scales, leading to scaling regimes with signatures of chaos at large scales and an apparently random behavior at small scales. These features are usually investigated quantitatively…
Fractals are ubiquitous natural emergences that have gained increased attention in engineering applications, thanks to recent technological advancements enabling the fabrication of structures spanning across many spatial scales. We show how…
The theory of p-adic fractal strings and their complex dimensions was developed by the first two authors in [17, 18, 19], particularly in the self-similar case, in parallel with its archimedean (or real) counterpart developed by the first…
The developing structure in systems of compacting ductile grains were studied experimentally in two and three dimensions. In both dimensions, the peaks of the radial distribution function were reduced, broadened, and shifted compared with…
In the present article, topological, metric, and fractal properties of certain sets are investigated. These sets are images of sets whose elements have restrictions on using digits or combinations of digits in own s-adic representations,…
We consider cosmological models based on the spectral action formulation of (modified) gravity. We analyze the coupled effects, in this model, of the presence of nontrivial cosmic topology and of fractality in the large scale structure of…
An exact analytical analysis of anomalous diffusion on a fractal mesh is presented. The fractal mesh structure is a direct product of two fractal sets which belong to a main branch of backbones and side branch of fingers. The fractal sets…
The development of algorithmic fractal dimensions in this century has had many fruitful interactions with geometric measure theory, especially fractal geometry in Euclidean spaces. We survey these developments, with emphasis on connections…
A simple method of calculating the Hausdorff-Besicovitch dimension of the Kronecker Product based fractals is presented together with a compact R script realizing it. The proposed new formula is based on traditionally used values of the…
Fractal dimensions have been used as a quantitative measure for structure of eigenstates of quantum many-body systems, useful for comparison to random matrix theory predictions or to distinguish many-body localized systems from chaotic…
The fractal dimension growth of urban form can be described with sigmoid functions such as logistic function due to squashing effect. The sigmoid curves of fractal dimension suggest a type of spatial replacement dynamics of urban evolution.…
For a large class of self-similar sets F in R^d analogues of the higher order mean curvatures of differentiable submanifolds are introduced, in particular, the fractal Gauss-type curvature. They are shown to be the densities of associated…
In this paper, we pose a hypothesis that the structure of communities in complex networks may result from their latent fractal properties. This hypothesis is based not only on the general observation that many real networks have multilevel…