Related papers: A Random Multifractal Tilling
Extensions of the fractional Brownian fields are constructed over a complete Riemannian manifold. This construction is carried out for the full range of the Hurst parameter $\alpha\in(0,1)$. In particular, we establish existence,…
We analyze invariant measures of two coupled piecewise linear and everywhere expanding maps on the synchronization manifold. We observe that though the individual maps have simple and smooth functions as their stationary densities, they…
For a Borel measure and a sequence of partitions on the unit interval, we define a multifractal spectrum based on coarse Holder regularity. Specifically, the coarse Holder regularity values attained by a given measure and with respect to a…
We consider here square tilings of the plane. By extending the formalism introduced in [3] we build a correspondence between plane maps endowed with an harmonic vector and square tilings satisfying a condition of regularity. In the case of…
Cohesive particles form agglomerates that are usually very porous. Their geometry, particularly their fractal dimension, depends on the agglomeration process (diffusion-limited or ballistic growth by adding single particles or…
We develop a recursive formula for counting the number of rectangulations of a square, i.e the number of combinatorially distinct tilings of a square by rectangles. Our formula specializes to give a formula counting generic rectangulations,…
This paper presents a detailed symbolic approach to the study of self-similar tilings. It uses properties of addresses associated with graph-directed iterated function systems to establish conjugacy properties of tiling spaces. Tiles may be…
Given a triangle ABC, we derive the probability distribution function and the moments of the area of an inscribed triangle RST whose vertices are uniformly distributed on AB, BC, and CA. The theoretical results are confirmed by a Monte…
A tiling is a decomposition of a polygon into finitely many non-overlapping triangles. We prove that if a regular n-gon, $n \geq 5$, $n \neq 28$, can be tiled with similar right triangles, then one of the angles of these triangles is in…
A method is established which allows the calculation of the walk dimension for Sierpinski-type multifractals. The multifractal scaling behaviour of the average time needed to cover a distance in the mentionned multifractals is shown. For…
We introduce a duality for Affine Iterated Function Systems (AIFS) which is naturally motivated by group duality in the context of traditional harmonic analysis. Our affine systems yield fractals defined by iteration of contractive affine…
The Spectre is an aperiodic monotile for the Euclidean plane that is truly chiral in the sense that it tiles the plane without any need for a reflected tile. The topological and dynamical properties of the Spectre tilings are very similar…
Although the theory of self-affine tiles and the theory of Rauzy fractals are quite different from each other, they have some common features. Both, self-affine tiles and Rauzy fractals have tiling properties and these tiling properties can…
A tiling of the unit square is an MTP tiling if the smallest tile can tile all the other tiles. We look at the function $f(n)=\max \sum s_i$, where $s_i$ is the side length of the $i$th tile and the sum is taken over all MTP tilings with…
A random intersection graph is constructed by assigning independently to each vertex a subset of a given set and drawing an edge between two vertices if and only if their respective subsets intersect. In this paper a model is developed in…
Complex networks have recently attracted much attention in diverse areas of science and technology. Many networks such as the WWW and biological networks are known to display spatial heterogeneity which can be characterized by their fractal…
A tiling is a cover of R^d by tiles such as polygons that overlap only on their borders. A patch is a configuration consisting of finitely many tiles that appears in tilings. From a tiling, we can construct a dynamical system which encodes…
We exhibit a characteristic structure of the class of all regular graphs of degree d that stems from the spectra of their adjacency matrices. The structure has a fractal threadlike appearance. Points with coordinates given by the mean and…
Tile the unit square with $n$ small squares. We determine the minimum of the sum of the side lengths of the $n$ small squares, where the minimum is taken over all tilings of the unit square with $n$ squares.
A numerical study is made of the spectra of a tight-binding hamiltonian on square approximants of the quasiperiodic octagonal tiling. Tilings may be pure or random, with different degrees of phason disorder considered. The level statistics…