Aperiodic sets of square tiles with colored corners (2006)
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by
Ares Lagae
,
Jarkko Kari
,
Philip Dutré
| Citations: | 3 - 2 self |
BibTeX
@TECHREPORT{Lagae06aperiodicsets,
author = {Ares Lagae and Jarkko Kari and Philip Dutré},
title = {Aperiodic sets of square tiles with colored corners},
institution = {},
year = {2006}
}
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Abstract
In this paper we formalize the concept of square tiles with colored corners, a new kind of tiles closely related to Wang tiles. We construct aperiodic sets of square tiles with colored corners and several new aperiodic sets of Wang tiles using isomorphisms between tilings. The smallest aperiodic set of square tiles with colored corners we have created consists of 44 tiles over 6 colors.
Citations
| 242 | Undecidability of the domino problem - Berger - 1966 |
| 103 | Wang tiles for image and texture generation - Cohen, Shade, et al. - 2003 |
| 35 | Proving theorems by pattern recognition ii - Wang - 1961 |
| 28 | Tiled blue noise samples - Hiller, Deussen, et al. - 2001 |
| 25 | A small aperiodic set of wang tiles - Kari - 1996 |
| 24 | Aperiodic texture mapping - Stam - 1997 |
| 19 | Tile-based texture mapping on graphics hardware - Wei - 2004 |
| 15 | DUTRÉ P.: A procedural object distribution function - LAGAE |
| 11 | An alternative for wang tiles: Colored edges versus colored corners - Lagae, Dutré - 2006 |
| 9 | logic and computers - Games - 1965 |
| 6 | An aperiodic set of 13 Wang tiles. Discrete Mathematics - Culik - 1996 |
