  The Fisher-Shannon complexity is used to quantitatively estimate the
contribution of relativistic effects to on the internal disorder of
Klein-Gordon single-particle Coulomb systems which is manifest in the rich
variety of three-dimensional geometries of its corresponding quantum-mechanical
probability density. It is observed that, contrary to the non-relativistic
case, the Fisher-Shannon complexity of these relativistic systems does depend
on the potential strength (nuclear charge). This is numerically illustrated for
pionic atoms. Moreover, its variation with the quantum numbers (n, l, m) is
analysed in various ground and excited states. It is found that the
relativistic effects enhance when n and/or l are decreasing.
