Related papers: Freeform Islamic Geometric Patterns
One of the best things about geometry is that it's cool! Geometry enables us to create incredible designs and astounding patterns. This article shows how to use a simple technique (iteration) to create designs that are both cool and…
In this paper we present two new ideas for generating star patterns and filling the gaps during the tile operation. Firstly, we introduce a novel parametric method based on concentric circles for generating stars and rosettes. Using…
For centuries, human civilizations devised metal forming techniques to make tools and items; yet, customized metal forming remains costly and intricate. Laser-forming origami} (lasergami) is a metal forming process where a laser beam cuts…
This article studies a large, general class of orthogonal polytopes which we may call "generic orthotopes". These objects emerged from a desire to represent a Coxeter complex by an orthogonal polytope that is particularly nice with respect…
In this paper, we present a new polygonal finite element method, called the Zipped Finite Element Method, for star-shaped polygons. The proposed approach constructs high-order shape functions as linear combinations of standard finite…
Phyllotactic patterns, i.e. regular arrangements of leaves or seeds around a plant stem, are fascinating examples of complex structures encountered in Nature. In botany, their symmetries develop when a new primordium periodically grows in…
Multicellular rosettes are observed in different situations such as morphogenesis, wound healing, and cancer progression. While some molecular insights have been gained to explain the presence of these assemblies of five or more cells…
Block designs are combinatorial structures in which each pair of a set of varieties appears together in a fixed number of blocks. Complete graphs are graphs in which every pair of vertices are adjacent. We present some new constructions of…
The Rouse-Ham model is a simple yet useful dynamics model for an unentangled branched polymer. In this work, we study the normal modes of the Rouse-Ham type coarse-grained symmetric star polymer model. We model a star polymer by connecting…
Multiple loop formation in polymer macromolecules is an important feature of the chromatin organization and DNA compactification in the nuclei. We analyze the size and shape characteristics of complex polymer structures, containing in…
A harmonic mapping is a univalent harmonic function of one complex variable. We define a family of harmonic mappings on the unit disk whose images are rotationally symmetric rosettes with $n$ cusps or n nodes, where $n \ge 3$. These…
We give a new combinatorial characterization of the big height of a squarefree monomial ideal leading to a new bound for the projective dimension of a monomial ideal.
The entries of frieze patterns may be interpreted as coordinates of roots of a finite Weyl groupoid of rank two. We prove the existence of maximal elements in their root posets and classify those frieze patterns which can be used to build…
Kirigami, the art of paper cutting, has become a paradigm for mechanical metamaterials in recent years. The basic building blocks of any kirigami structures are repetitive deployable patterns that derive inspiration from geometric art forms…
We study polygon spaces arising from planar configurations of necklaces with some of the beads fixed and some of the beads sliding freely. These spaces include configuration spaces of flexible polygons and some other natural polygon spaces.…
This paper examines the structure of poset matrices by formulating a set of new construction rules for this purpose. In this direction, the technique of partial composition operation will be introduced as the basis for the construction of…
A geometrical pattern is a set of points with all pairwise distances (or, more generally, relative distances) specified. Finding matches to such patterns has applications to spatial data in seismic, astronomical, and transportation…
Different aspects of application of non-Euclidian geometries in architectural compositions are considered. These aspects are illustrated by examples of Armenian (medieval and contemporary) architectural compositions.
We introduce iposets---posets with interfaces---equipped with a novel gluing composition along interfaces and the standard parallel composition. We study their basic algebraic properties as well as the hierarchy of gluing-parallel posets…
Polymeric micelles are used in a variety of applications, with the micelle's shape often playing an important role. Consequently, a scheme to design micelles of arbitrary shape is desirable. In this paper, we consider micelles formed from a…