Error diffusion on simplices: The structure of bounded invariant tiles
| Autor: | Tomasz Nowicki, Roy L. Adler, Grzegorz Świrszcz, Shmuel Winograd, Charles Tresser |
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| Rok vydání: | 2018 |
| Předmět: |
Discrete mathematics
Simplex Dynamical systems theory General Mathematics 010102 general mathematics Polytope 0102 computer and information sciences 01 natural sciences Combinatorics 010201 computation theory & mathematics Bounded function visual_art visual_art.visual_art_medium Mathematics::Metric Geometry Ergodic theory Tile 0101 mathematics Invariant (mathematics) Voronoi diagram Mathematics |
| Zdroj: | Indagationes Mathematicae. 29:831-841 |
| ISSN: | 0019-3577 |
| DOI: | 10.1016/j.indag.2017.10.001 |
| Popis: | This is a companion paper to Adleret al. (in press, 2015). There, we proved the existence of an absorbing invariant tile for the Error Diffusion dynamics on an acute simplex when the input is constant and “ergodic” and we discuss the geometry of this tile. Under the same assumptions we prove here that said invariant tile (a fundamental set of the lattice generated by the vertices of the simplex) which is a finite union of polytopes have the property that any union of the intersections of the tile with the Voronoi regions of the vertices is a tile for a different, explicitly defined lattice. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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