Ten Colours in Quasiperiodic and Regular Hyperbolic Tilings

نویسندگان

  • R. LÜCK
  • D. FRETTLÖH
چکیده

Colour symmetries with ten colours are presented for different tilings. In many cases, the existence of these colourings were predicted by group theoretical methods. Only in a few cases explicit constructions were known, sometimes using combination of two-colour and five-colour symmetries. Here we present explicit constructions of several of the predicted colourings for the first time, and discuss them in contrast to already known colourings with ten colours.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Tiling the Hyperbolic Plane with a Single Pentagonal Tile

In this paper, we study the number of tilings of the hyperbolic plane that can be constructed, starting from a single pentagonal tile, the only permitted transformations on the basic tile being the replication by displacement along the lines of the pentagrid. We obtain that there is no such tiling with five colours, that there are exactly two of them with four colours and a single trivial tilin...

متن کامل

Self-avoiding walks and polygons on quasiperiodic tilings

We enumerate self-avoiding walks and polygons, counted by perimeter, on the quasiperiodic rhombic Penrose and Ammann-Beenker tilings, thereby considerably extending previous results. In contrast to similar problems on regular lattices, these numbers depend on the chosen initial vertex. We compare different ways of counting and demonstrate that suitable averaging improves convergence to the asym...

متن کامل

Fibonacci Type Coding for the Regular Rectangular Tilings of the Hyperbolic Plane

The study of cellular automata (CA) on tilings of hyperbolic plane was initiated in [6]. Appropriate tools were developed which allow us to produce linear algorithms to implement cellular automata on the tiling of the hyperbolic plane with the regular rectangular pentagons, [8, 10]. In this paper we modify and improve these tools, generalise the algorithms and develop them for tilings of the hy...

متن کامل

Outer Billiards and Tilings of the Hyperbolic Plane

In this paper we present new results regarding the periodicity of outer billiards in the hyperbolic plane around polygonal tables which are tiles in regular two-piece tilings of the hyperbolic plane.

متن کامل

Gap Labelling for Schrödinger Operators on Quasiperiodic Tilings

For a large class of tilings, including those which are obtained by the generalized dual method from regular grids, it is shown that their algebra is stably isomorphic to a crossed product with Z Z . For d ≤ 3 this in particular enlarges the class of tilings of which can be shown that a set of possible gap labels is completely determined by an invariant measure on the hull.

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2008