منابع مشابه
Non-Repetitive Tilings
In 1906 Axel Thue showed how to construct an infinite non-repetitive (or squarefree) word on an alphabet of size 3. Since then this result has been rediscovered many times and extended in many ways. We present a two-dimensional version of this result. We show how to construct a rectangular tiling of the plane using 5 symbols which has the property that lines of tiles which are horizontal, verti...
متن کاملNon-Periodic Corner Tilings in Computer Graphics
Rendering computer-generated images is both memory and runtime intensive. This is particularly true in realtime computer graphics where large amounts of content have to be produced very quickly and from limited data. Tile-based methods offer a solution to this problem by generating large portions of a specific content out of a much smaller data set of tiles. This dissertation investigates the u...
متن کاملTilings from some non-irreducible, Pisot substitutions
A generating method of self-affine tilings for Pisot, unimodular, irreducible substitutions, as well as the fact that the associated substitution dynamical systems are isomorphic to rotations on the torus are established in [AI01]. The aim of this paper is to extend these facts in the case where the characteristic polynomial of a substitution is non-irreducible for a special class of substituti...
متن کاملTilings from non-Pisot unimodular matrices
Using the unimodular Pisot substitution of the free monoid on d letters, the existence of graph-directed self-similar sets fXigi1⁄41; 2;...; d satisfying the set equation (0.0.1) with the positive measure on the A-invariant contracting plane P is well-known, where A is the incidence matrix of the substitution. Moreover, under some conditions, the set fXigi1⁄41; 2;...; d is the prototile of the ...
متن کاملQuasiperiodicity and Non-computability in Tilings
We study tilings of the plane that combine strong properties of different nature: combinatorial and algorithmic. We prove the existence of a tile set that accepts only quasiperiodic and non-recursive tilings. Our construction is based on the fixed point construction [12]; we improve this general technique and make it enforce the property of local regularity of tilings needed for quasiperiodicit...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 2002
ISSN: 1077-8926
DOI: 10.37236/1644