Related papers: Tiling Iterated Function Systems
Differentiable conjugacies link dynamical systems that share properties such as the stability multipliers of corresponding orbits. It provides a stronger classification than topological conjugacy, which only requires qualitative similarity.…
We study set systems formed by neighborhoods in graphs of bounded twin-width. We start by proving that such graphs have linear neighborhood complexity, in analogy to previous results concerning graphs from classes with bounded expansion and…
The conjugate function method is an algorithm for numerical computation of conformal mappings for simply and multiply connected domains on surfaces. In this paper the conjugate function method, earlier used for simply connected domains, is…
The concept of star-duality is described for self-similar cut-and-project tilings in arbitrary dimensions. This generalises Thurston's concept of a Galois-dual tiling. The dual tilings of the Penrose tilings as well as the Ammann-Beenker…
This paper investigates spaces equipped with a family of metric-like functions satisfying certain axioms. These functions provide a unified framework for defining topology, uniformity, and diffeology. The framework is based on a family of…
Fractal interpolation function (FIF) is a special type of continuous function which interpolates certain data set and the attractor of the Iterated function system (IFS) corresponding to the data set is the graph of the FIF. Coalescence…
New scalar structure functions with different sign-symmetry properties are defined. These structure functions possess different scaling exponents even when their order is the same. Their scaling properties are investigated for second and…
The problem of finding graph structure of functions commuting with a given function in terms of their functional graphs is considered. Structure of functional graphs of commuting functions is described. The problem is reduced to describing…
On the one hand, the dynamical interior of a self-similar set with open set condition is the complement of the dynamical boundary. On the other hand, the dynamical interior is the recurrent set of the magnification flow. For a finite type…
Let $X$ be a measure space with a measure-preserving action $(g,x) \mapsto g \cdot x$ of an abelian group $G$. We consider the problem of understanding the structure of measurable tilings $F \odot A = X$ of $X$ by a measurable tile $A…
In the process of measuring objects with local self-similarity, such as satellite images or coastlines, we obtain a data set with both local self-similarity and uncertainty. To better interpolate such data sets, an interpolation function…
We introduce and study the number of tilings of unit height rectangles with irrational tiles. We prove that the class of sequences of these numbers coincides with the class of diagonals of N-rational generating functions and a class of…
Given a tiling of a 2D grid with several types of tiles, we can count for every row and column how many tiles of each type it intersects. These numbers are called the_projections_. We are interested in the problem of reconstructing a tiling…
We study the problem of finding a function $f$ with ``small support'' that simultaneously tiles with finitely many lattices $\Lambda_1, \ldots, \Lambda_N$ in $d$-dimensional Euclidean spaces. We prove several results, both upper bounds…
In this paper we continue the study of dilatation structures, introduced in math.MG/0608536 . A dilatation structure on a metric space is a kind of enhanced self-similarity. By way of examples this is explained here with the help of the…
The ability to design and synthesize ever more complicated colloidal particles opens the possibility of self-assembling a zoo of complex structures, including those with one or more self-limited length scales. An undesirable feature of…
We offer some partition functions related to ternary quadratic forms, and note on their upper bounds and related properties. We offer these results as an application of a simple method related to conjugate Bailey pairs presented in a prior…
We study multiplicative nested sums, which are generalizations of harmonic sums, and provide a calculation through multiplication of index matrices. Special cases interpret the index matrices as stochastic transition matrices of random…
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,…
Pairs of graded graphs, together with the Fomin property of graded graph duality, are rich combinatorial structures providing among other a framework for enumeration. The prototypical example is the one of the Young graded graph of integer…