  We investigate the asymptotic behavior of minimal $N$-point Riesz $s$-energy
on fractal sets of non-integer dimension, with algebraically dependent
contraction ratios. For $s$ bigger than the dimension of the set $A$, we prove
the asymptotic behavior of the minimal $N$-point Riesz $s$-energy of $A$ along
explicit subsequences, but we show that the general asymptotic behavior does
not exist.
