  We investigate properties of minimal $N$-point Riesz $s$-energy on fractal
sets of non-integer dimension, as well as asymptotic behavior of $N$-point
configurations that minimize this energy. For $s$ bigger than the dimension of
the set $A$, we constructively prove a negative result concerning the
asymptotic behavior (namely, its nonexistence) of the minimal $N$-point Riesz
$s$-energy of $A$, but we show that the asymptotic exists over reasonable
sub-sequences of $N$. Furthermore, we give a short proof of a result concerning
asymptotic behavior of configurations that minimize the discrete Riesz
$s$-energy.
