Box Counting Dimension of the Union L of Trinomial Curves When α ≥ 1

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.