### Fractal 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 $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.

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.

#### Full Text:

PDFDOI: https://doi.org/10.52846/ami.v47i1.1300