Shape Tiling
نویسندگان
چکیده
منابع مشابه
Shape tiling
definition of packing and tiling.) Two recent papers by Freiling & Rinne 1994, and by Laczkovich & Szekeres 1995, turn the question around: For which sidelengths, s, can the square be packed by rectangles similar to 1 × s and s × 1? Employing a Dehn-functional and a theorem of Wall1945, they give this astonishing answer: Iff s is algebraic over , and all of its conjugates in the complex plane h...
متن کاملTiling spaces, codimension one attractors and shape
We establish a close relationship between, on the one hand, expanding, codimension one attractors of diffeomorphisms on closed manifolds (examples of so-called strange attractors), and, on the other, spaces which arise in the study of aperiodic tilings. We show that every such orientable attractor is homeomorphic to a tiling space of either a substitution or a projection tiling, depending on it...
متن کاملWhen Shape Matters: Deformations of Tiling Spaces
We investigate the dynamics of tiling dynamical systems and their deformations. If two tiling systems have identical combinatorics, then the tiling spaces are homeomorphic, but their dynamical properties may differ. There is a natural map I from the parameter space of possible shapes of tiles to H of a model tiling space, with values in R. Two tiling spaces that have the same image under I are ...
متن کاملEffect of shape on the self-assembly of faceted patchy nanoplates with irregular shape into tiling patterns.
Recent reports of the synthesis and assembly of faceted nanoplates with a wide range of shapes and composition motivates the possibility of a new class of two-dimensional materials with specific patterns targeted for a host of exciting properties. Yet, studies of how nanoplate shape controls their assembly - knowledge necessary for their inverse design from target structures - has been performe...
متن کاملOptimal Tiling
Iteration space tiling is a common strategy used by parallelizing compilers to reduce communication overhead. We address the problem of determining the optimal tile size (which minimizes the total execution time of the program), for a particular program schema. We use a realistic model of the architecture which accounts for coprocessors that permit overlapping of communication and computation, ...
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ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 1996
ISSN: 1077-8926
DOI: 10.37236/1327