Article
Geometric Palindromic Closure
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Abstract
We define, through a set of symmetries, an incremental construc- tion of geometric objects in Zd. This construction is directed by a word over the alphabet {1, . . . , d}. These objects are composed of d disjoint components linked by the origin and enjoy the nice property that each component has a central sym- metry as well as the global object. This construction may be seen as a geometric palindromic closure. Among other objects, we get a 3 dimensional version of the Rauzy fractal. For the dimension 2, we show that our construction codes the standard discrete lines and is equivalent to the well known palindromic closure in combinatorics on words.
Keywords
palindromic closure, Sturmian sequences, Rauzy fractal, discrete plane.
Citation
Domenjoud, E. & Vuillon, L. (2012). Geometric palindromic closure. Uniform Distribution Theory, 7(2), 109–140.
E. Domenjoud and L. Vuillon, “Geometric palindromic closure,” Uniform Distribution Theory, vol. 7, no. 2, pp. 109–140, 2012.
Domenjoud E, Vuillon L. Geometric palindromic closure. Uniform Distribution Theory. 2012;7(2):109–140.
Domenjoud, E. and Vuillon, L. (2012), ‘Geometric palindromic closure’, Uniform Distribution Theory, 7(2), pp. 109–140.
Domenjoud, Eric, and Laurent Vuillon. “Geometric Palindromic Closure.” Uniform Distribution Theory, vol. 7, no. 2, 2012, pp. 109–140.
Domenjoud, Eric, and Laurent Vuillon. “Geometric Palindromic Closure.” Uniform Distribution Theory 7, no. 2 (2012): 109–140.
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Published by: Engineering Journals
