Related papers: The hat polykite as an Iterated Function System
Ackermann's function can be expressed using an iterative algorithm, which essentially takes the form of a term rewriting system. Although the termination of this algorithm is far from obvious, its equivalence to the traditional recursive…
We study enumerations of Dyck and ballot tilings, which are tilings of a region determined by two Dyck or ballot paths. We give bijective proofs to two formulae of enumerations of Dyck tilings through Hermite histories. We show that one of…
In this paper, we introduce a generalization of a class of tilings which appear in the literature: the tilings over which a height function can be defined (for example, the famous tilings of polyominoes with dominoes). We show that many…
We propose a notion of iterating functions $f:X^{k}\rightarrow X$ in a way that represents recurrence relations of the form $a_{n+k}=f(a_{n},a_{n+1},...,a_{n+k-1})$. We define a function as $n$-involutory when its $n$th iterate is the…
Some linear dynamical systems over finite fields are studied and the self-similar character of their development is proved. Connections with aperiodic tilings, Delanoy numbers and other topics are also proved. The prime fields F_p have a…
We consider the models of distributed computation defined as subsets of the runs of the iterated immediate snapshot model. Given a task $T$ and a model $M$, we provide topological conditions for $T$ to be solvable in $M$. When applied to…
In this paper, we focus attention on extending the topological conjugacy of adding machine maps and minimal systems to iterated function systems. We provide necessary and sufficient conditions for an iterated function system to be…
Windowed recurrences are sliding window calculations where a function is applied iteratively across the window of data, and are ubiquitous throughout the natural, social, and computational sciences. In this monograph we explore the…
We give an explicit sequence of polarizations such that for every measurable function, the sequence of iterated polarizations converge to the symmetric rearrangement of the initial function.
Starting with the recursive extended Euclid's algorithm, we apply a systematic approach using matrix notation to transform it into an iterative algorithm. The partial correctness proof derived from the transformation turns out to be very…
This paper discusses iterated monodromy groups for transcendental functions. We show that for every post-singularly finite entire transcendental function, the iterated monodromy action can be described by bounded activity automata of a…
We study random independent and identically distributed iterations of functions from an iterated function system of homeomorphisms on the circle which is minimal. We show how such systems can be analyzed in terms of iterated function…
Although power laws of the Zipf type have been used by many workers to fit rank distributions in different fields like in economy, geophysics, genetics, soft-matter, networks etc., these fits usually fail at the tails. Some distributions…
In this paper we extend counting of traversing Hamiltonian cycles from 2-tiled graphs to generalized tiled graphs. We further show that, for a fixed finite set of tiles, counting traversing Hamiltonian cycles can be done in linear time with…
We prove linearly repetitive Delone systems have finitely many Delone system factors up to conjugacy. This result is also applicable to linearly repetitive tiling systems.
The recently discovered Hat tiling admits a 4-dimensional family of shape deformations, including the 1-parameter family already known to yield alternate monotiles. The continuous hulls resulting from these tilings are all topologically…
In this article, we establish a class of new projected type iteration methods based on matrix spitting for solving the linear complementarity problem. Also, we provide a sufficient condition for the convergence analysis when the system…
In this paper, we study the structure of the set of tilings produced by any given tile-set. For better understanding this structure, we address the set of finite patterns that each tiling contains. This set of patterns can be analyzed in…
This paper presents a novel set-based computing method, called interval superposition arithmetic, for enclosing the image set of multivariate factorable functions on a given domain. In order to construct such enclosures, the proposed…
We consider tilings of Euclidean spaces by polygons or polyhedra, in particular, tilings made by a substitution process, such as the Penrose tilings of the plane. We define an isomorphism invariant related to a subgroup of rotations and…