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Box Counting Dimension of the Union L of Trinomial Curves When α ≥ 1
Abstract:In the present work, we consider one category of curves denoted by L(p, k, r, n). These curves are continuous arcs which are trajectories of roots of the trinomial equation zn = αzk + (1 − α), where z is a complex number, n and k are two integers such that 1 ≤ k ≤ n − 1 and α is a real parameter greater than 1. Denoting by L the union of all trinomial curves L(p, k, r, n) and using the box counting dimension as fractal dimension, we will prove that the dimension of L is equal to 3/2.
Digital Object Identifier (DOI): doi.org/10.5281/zenodo.2576978Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 491
 S. Dubuc and M. Zaoui, The fractal dimension of a union of trinomial arcs, World Scientific Publishing Company, Fractals, Vol. 4, No. 4 (1996), 555 - 562.
 K. J. Falconer. Fractal Geometry : Mathematical Foundations and Applications. John Wiley & Sons, England, 1990.
 H. Fell. The Geometry of Zeros of Trinomial Equations. Rendiconti del Circolo Matematico di Palermo, Serie II, Tomo XXIX, pp. 303-336, 1980.
 K. Lamrini Uahabi, A Note on the Trinomial Curves L(p, k, r, n). International Mathematical Forum, Vol.4, no. 2, pp. 67-71, 2009.
 C. Tricot. Courbes et Dimension Fractale. Springer-Verlag, Editions Sciences et Culture, Paris, France, 1993.