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On the Tribonacci fractals

T. Sellami1

  1. Dept. of Mathematics, Faculty of sciences of Sfax, Sfax University, Sfax, Tunisia.

Section:Review Paper, Product Type: Isroset-Journal
Vol.5 , Issue.2 , pp.70-74, Apr-2018


CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v5i2.7074


Online published on Apr 30, 2018


Copyright © T. Sellami . This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
 

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IEEE Style Citation: T. Sellami, “On the Tribonacci fractals,” International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.5, Issue.2, pp.70-74, 2018.

MLA Style Citation: T. Sellami "On the Tribonacci fractals." International Journal of Scientific Research in Mathematical and Statistical Sciences 5.2 (2018): 70-74.

APA Style Citation: T. Sellami, (2018). On the Tribonacci fractals. International Journal of Scientific Research in Mathematical and Statistical Sciences, 5(2), 70-74.

BibTex Style Citation:
@article{Sellami_2018,
author = {T. Sellami},
title = {On the Tribonacci fractals},
journal = {International Journal of Scientific Research in Mathematical and Statistical Sciences},
issue_date = {4 2018},
volume = {5},
Issue = {2},
month = {4},
year = {2018},
issn = {2347-2693},
pages = {70-74},
url = {https://www.isroset.org/journal/IJSRMSS/full_paper_view.php?paper_id=581},
doi = {https://doi.org/10.26438/ijcse/v5i2.7074}
publisher = {IJCSE, Indore, INDIA},
}

RIS Style Citation:
TY - JOUR
DO = {https://doi.org/10.26438/ijcse/v5i2.7074}
UR - https://www.isroset.org/journal/IJSRMSS/full_paper_view.php?paper_id=581
TI - On the Tribonacci fractals
T2 - International Journal of Scientific Research in Mathematical and Statistical Sciences
AU - T. Sellami
PY - 2018
DA - 2018/04/30
PB - IJCSE, Indore, INDIA
SP - 70-74
IS - 2
VL - 5
SN - 2347-2693
ER -

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Abstract :
We consider the two tribonacci substitutions, a → ab, b → ac, c → a and a → ab, b → ca, c → a. In this paper we give some properties for the Tribonacci fractals, and its associated intersection fractal. We show in more details intersections of subtiles.

Key-Words / Index Term :
Rauzy fractals, Substitution dynamical systems, balanced pairs algorithm

References :
[1] P. Arnoux and S. Ito "Pisot substitutions and Rauzy fractals" Bull. Belg. Math. Soc. Simon Stevin 8: 181--207 (2001).
[2] M.Barge and B.Diamond. "Coincidence for substitutions of Pisot Type". Bell.Soc.Math. France, 130:619-626, 2002.
[3] Marcy Barge and Jarek Kwapisz, "Geometric theory of unimodular Pisot substitutions". American journal of mathematics(Print) 128:55, 1219-1282.
[4] Vicent Canterini and Anne Siegel : {"Automate des préfixes-suffixes associé une substitution primitive".J. Théor. Nombres Bordeaux 13, no. 2, 353--369, 2001.
[5] Amara Chandoul : {"On the continued fraction of fixed period in finite filds", Canadian mathematical bulletin.}.
[6] Amara Chandoul : {"The Pell Equation", Advances in Pure Mathematics..}
[7] Amara Chandoul : {"On the continued fraction over the filds of formal power series" , Canadian mathematical bulletin.}
[8] Amara Chandoul : {"On Polynomials solutions of quadratic Diophantine Equations.", Advances in Pure Mathematics..}
[9] F. M. Dekking, recurrent sets, Adv. in Math. 44 (1982), no. 1, 78-104. MR 84 : 52023.
[10] P. Fogg, "Substitutions in dynamics, arithmetics and combinatorics" (Lecture Botes in Mathematics, Vol. 1794).
[11] J. M. Luck, C. Godrѐche and A. Janner and T. Janssen, "The nature of the atomic surfaces of quasiperiodic self similar structures", J. Phys. A : Math. Gen. 26 : 1951-1999 (1993).
[12] A. Messaoudi: "Propriétés arithmétiques et dynamiques du fractal de Rauzy", journal de Théorie des nombres de bordeaux, 10, 1998, 135-162.
[13] G. Rauzy: "Nombre algébrique et substitution", Bull.Soc.Math. France 110 (1982), 147-178.
[14] M. Queffelec, "Substitution dynamical system", Spectra analysis, lecture note in mathematics, 1294, Springer-Verlag, Berlin, 1987.
[15] Anne Siegel: "Autour des fractals de Rauzy", Journées Femmes et Mathématiques, Paris (03/2002).
[16] Anne Siegel and Jorg M.Thuswaldner: "Topological proprieties of Rauzy fractal", Mémoires de la SMF.
[17] Victor F.Sirvent: "The common dynamics of the tribonacci substitutions", Bull. Belg.Math..Soc. 7 (2000), 571-582.
[18] B. Sing and V. Sirvent: "Geometry of the common dynamics of flipped Pisot substitution", Monatshefte für Mathematik, 155 (2008), 431-448.
[19] Victor Sirvent and yang Sirvent, "Self affine tiling via substitution dynamical systems and Rauzy fractal". Pacific journal of mathematics Vol 206, N 2, 2002.

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