اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدDappled tiling
342
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
We consider a certain tiling problem of a planar region in which there are no long horizontal or vertical strips consisting of copies of the same tile. Intuitively speaking, we would like to create a dappled pattern with two or more kinds of tiles. We give an efficient algorithm to turn any tiling into one satisfying the condition, and discuss its applications in texturing.
قيم البحث
اقرأ أيضاً
The Wang tiling is a classical problem in combinatorics. A major theoretical question is to find a (small) set of tiles which tiles the plane only aperiodically. In this case, resulting tilings are rather restrictive. On the other hand, Wang tiles ar
e used as a tool to generate textures and patterns in computer graphics. In these applications, a set of tiles is normally chosen so that it tiles the plane or its sub-regions easily in many different ways. With computer graphics applications in mind, we introduce a class of such tileset, which we call sequentially permissive tilesets, and consider tiling problems with constrained boundary. We apply our methodology to a special set of Wang tiles, called Brick Wang tiles, introduced by Derouet-Jourdan et al. in 2015 to model wall patterns. We generalise their result by providing a linear algorithm to decide and solve the tiling problem for arbitrary planar regions with holes.
We exhibit a weakly aperiodic tile set for Baumslag-Solitar groups, and prove that the domino problem is undecidable on these groups. A consequence of our construction is the existence of an arecursive tile set on Baumslag-Solitar groups.
We prove Gibbs distribution of two-state spin systems(also known as binary Markov random fields) without hard constrains on a tree exhibits strong spatial mixing(also known as strong correlation decay), under the assumption that, for arbitrary `exter
nal field, the absolute value of `inverse temperature is small, or the `external field is uniformly large or small. The first condition on `inverse temperature is tight if the distribution is restricted to ferromagnetic or antiferromagnetic Ising models. Thanks to Weitzs self-avoiding tree, we extends the result for sparse on average graphs, which generalizes part of the recent work of Mossel and Slycite{MS08}, who proved the strong spatial mixing property for ferromagnetic Ising model. Our proof yields a different approach, carefully exploiting the monotonicity of local recursion. To our best knowledge, the second condition of `external field for strong spatial mixing in this paper is first considered and stated in term of `maximum average degree and `interaction energy. As an application, we present an FPTAS for partition functions of two-state spin models without hard constrains under the above assumptions in a general family of graphs including interesting bounded degree graphs.
Motivated by applications in reliable and secure communication, we address the problem of tiling (or partitioning) a finite constellation in $mathbb{Z}_{2^L}^n$ by subsets, in the case that the constellation does not possess an abelian group structur
e. The property that we do require is that the constellation is generated by a linear code through an injective mapping. The intrinsic relation between the code and the constellation provides a sufficient condition for a tiling to exist. We also present a necessary condition. Inspired by a result in group theory, we discuss results on tiling for the particular case when the finer constellation is an abelian group as well.
In this paper a closed form expression for the number of tilings of an $ntimes n$ square border with $1times 1$ and $2times1$ cuisenaire rods is proved using a transition matrix approach. This problem is then generalised to $mtimes n$ rectangular bor
ders. The number of distinct tilings up to rotational symmetry is considered, and closed form expressions are given, in the case of a square border and in the case of a rectangular border. Finally, the number of distinct tilings up to dihedral symmetry is considered, and a closed form expression is given in the case of a square border.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
