  The Fisher-Shannon complexity plane is a powerful tool that represents
complex dynamics in a two-dimensional plane. It locates a dynamical system
based upon its entropy and its Fisher Information Measure (FIM). It has been
recently shown that, by using ordinal patterns to compute permutation entropy
and FIM, this plane unveils inner details of the structure underlying the
complex and chaotic dynamics of a system. In order to compute FIM, the order of
the patterns is very relevant. We analyze in detail the impact of the sorting
protocol used to calculate FIM using ordinal patterns. We show the importance
of a suitable choice, which can lead to saving computational resources, but
also to unveil details of the dynamics not accessible to other sorting
protocols. Our results agree with previous research, and common characteristic
fingerprints are found for the different chaotic maps studied. Our analysis
also reveals the fractal behavior of the chaotic maps studied. We extract some
underlying symmetries that allow us to simulate the behavior on the complexity
plane for a wide range of the control parameters in the chaotic regimes.
