  We investigate the set of invariant idempotent probabilities for countable
idempotent iterated function systems (IFS) defined in compact metric spaces. We
demonstrate that, with constant weights, there exists a unique invariant
idempotent probability. Utilizing Secelean's approach to countable IFSs, we
introduce partially finite idempotent IFSs and prove that the sequence of
invariant idempotent measures for these systems converges to the invariant
measure of the original countable IFS. We then apply these results to
approximate such measures with discrete systems, producing, in the
one-dimensional case, data series whose Higuchi fractal dimension can be
calculated. Finally, we provide numerical approximations for two-dimensional
cases and discuss the application of generalized Higuchi dimensions in these
scenarios.
