Kaoutar Lamrini Uahabi and Mohamed Atounti
Box Counting Dimension of the Union L of Trinomial Curves When α ≥ 1
44 - 47
2019
13
2
International Journal of Mathematical and Computational Sciences
https://publications.waset.org/pdf/10010081
https://publications.waset.org/vol/146
World Academy of Science, Engineering and Technology
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 &alpha;zk (1 &minus; &alpha;),
where z is a complex number, n and k are two integers such that
1 &le; k &le; n &minus; 1 and &alpha; 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 32.
Open Science Index 146, 2019