×

zbMATH — the first resource for mathematics

A self similar tiling generated by the minimal Pisot number. (English) Zbl 1024.11066
The paper deals with the study of a fractal boundary for a special case of tiles. The concepts adjacency and vertex are included too. In addition the boundary of tiles are 5 sets of Hausdorff dimension 1.10026.

MSC:
11R06 PV-numbers and generalizations; other special algebraic numbers; Mahler measure
11K16 Normal numbers, radix expansions, Pisot numbers, Salem numbers, good lattice points, etc.
11A63 Radix representation; digital problems
PDF BibTeX XML Cite
Full Text: EuDML
References:
[1] S. Akiyama: Pisot numbers and greedy algorithm. Number Theory, Diophantine, Computational and Algebraic Aspects, edited by K.Gyory, A. Petho and V.T. Sos, 9-21, de Gruyter, Berlin, New York (1998) · Zbl 0919.11063
[2] M. J. Bertin A. Decomps-Guilloux M. Grandet-Hugot M. Pathiaux-Delefosse J. P. Schreiber: Pisot and Salem Numbers. Birkhauser Verlag Basel-Boston-Berlin. (1992) · Zbl 0772.11041
[3] K. J. Falconer: Techniques in Fractal Geometry. John Wiley & Sons.(1997) · Zbl 0869.28003
[4] C. Frougny B. Solomyak: Finite beta-expansions. Ergod. Th. and Dynam. Sys. 12 (1992) 713-723 · Zbl 0814.68065 · doi:10.1017/S0143385700007057
[5] A. Messaoudi: Frontiere du fractal de Rauzy et systeme de numeration complexe. preprint. · Zbl 0968.28005 · eudml:207448
[6] W. Parry: On the \(\beta\)-expansions of real numbers. Acta Math. Acad. Sci. Hungar. 11 (1960) 269-278 · Zbl 0099.28103 · doi:10.1007/BF02020954
[7] G. Rauzy: Nombres Algebriques et substitutions. Bull. Soc. France 110 (1982), 147-178. · Zbl 0522.10032 · numdam:BSMF_1982__110__147_0 · eudml:87410
[8] W. P. Thurston: Groups, Tilings and Finite state automata. Summer 1989 AMS Colloquium lectures, Research Report GCG 1.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.