Fractal dimension of the union L of trinomial curves when α >= 1

Lamrini Kaoutar Uahabi, Mohamed Atounti


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 $z^n=\alpha
z^k+(1-\alpha )$, where z is a complex number, n and k are two
integers such that 1<= k<= n-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 3/2.

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