Related papers: Tiling Iterated Function Systems
We study the attractor of Iterated Function Systems composed of infinitely many affine, homogeneous maps. In the special case of second generation IFS, defined herein, we conjecture that the attractor consists of a finite number of…
Partitioning large matrices is an important problem in distributed linear algebra computing (used in ML among others). Briefly, our goal is to perform a sequence of matrix algebra operations in a distributed manner (whenever possible) on…
This paper studies properties of tilings of the plane by parallelograms. In particular it is established that in parallelogram tilings using a finite number of shapes all tiles occur in only finitely many orientations.
We investigate the use of iterated function system (IFS) models for data analysis. An IFS is a discrete dynamical system in which each time step corresponds to the application of one of a finite collection of maps. The maps, which represent…
It is proved that every pseudo-self-affine tiling in R^d is mutually locally derivable with a self-affine tiling. A characterization of pseudo-self-similar tilings in terms of derived Voronoi tessellations is a corollary. Previously, these…
We employ the notions of `sequential function' and `interrogation' (dialogue) in order to define new partial combinatory algebra structures on sets of functions. These structures are analyzed using J. Longley's preorder-enriched category of…
This paper is a survey, with few proofs, of ideas and notions related to self-similarity of groups, semi-groups and their actions. It attempts to relate these concepts to more familiar ones, such as fractals, self-similar sets, and…
The matching complex of a simple graph $G$ is a simplicial complex consisting of the matchings on $G$. Jeli\'c Milutinovi\'c et al. studied the matching complexes of the polygonal line tilings, and they gave a lower bound for the…
This paper deals with iteration stable (STIT) tessellations, and, more generally, with a certain class of tessellations that are infinitely divisible with respect to iteration. They form a new, rich and flexible class of spatio-temporal…
We give characterizations of unital uniform topological algebras and saturated locally multiplicatively convex algebras by means of multiplicative linear functionals. Some automatic continuity theorems in advertibly complete uniform…
In this paper, we consider a generalization of the Stirling number sequence of both kinds by using a specialization of a new family of symmetric functions. We give combinatorial interpretations for this symmetric functions by means of…
In this paper, we study cut sets of attractors of iteration function systems (IFS) in $\mathbb{R}^d$. Under natural conditions, we show that all irreducible cut sets of these attractors are perfect sets or single points. This leads to a…
We show how geometric methods from the general theory of fractal dimensions and iterated function systems can be deployed to study symbolic dynamics in the zero entropy regime. More precisely, we establish a dimensional characterization of…
We study the intimate relationship between the Penrose and the Taylor-Socolar tilings, within both the context of double hexagon tiles and the algebraic context of hierarchical inverse sequences of triangular lattices. This unified approach…
The multifractal structure underlying a self-similar measure stems directly from the weighted self-similar system (or weighted iterated function system) which is used to construct the measure. This follows much in the way that the dimension…
This survey is the continuation of a series of works aimed at applying tools from Singularity Theory to Differential Equations. More precisely, we utilize the powerfull Milnor's Fibration Theory to give geometric-topological classifications…
An effort has been made to show mathematicians some new ideas applied to image analysis. Gray images are presented as tilings. Based on topological properties of the tiling, a number of gray convex hulls: maximal, minimal, and oriented ones…
In this paper we will introduce the methodology of analysis of the convex hull of the attractors of iterated functional systems (IFS) - compact fixed sets of self-similarity mapping. The method is based on a function which for a direction,…
Some boundedness properties of function spaces (considered as topological groups) are studied.
In the first section we review recent results on the harmonic analysis of fractals generated by iterated function systems with emphasis on spectral duality. Classical harmonic analysis is typically based on groups whereas the fractals are…