  We report a study of overdamped Josephson junction arrays with the geometry
of periodically repeated Sierpinski gaskets. These model superconductors share
essential geometrical features with truly random (percolative) systems. When
exposed to a perpendicular magnetic field B, their euclidian or fractal
behavior depends on the relation between the intervortex distance (imposed by
B) and the size of a constituent gasket, and was explored with high-resolution
measurements of the sample magnetoinductance L(B). In terms of the frustration
parameter f expressing (in units of the superconducting flux quantum) the
magnetic flux threading an elementary triangular cell of a gasket, the
crossover between the two regimes occurs at f_{cN}=1/(2*4^{N}), where N is the
gasket order. In the fractal regime (f>f_{cN}) a sequence of equally spaced
structures corresponding to the set of states with unit cells not larger than a
single gasket is observed at multiples of f_{cN}, as predicted by theory. The
fine structure of L(f) radically changes in the euclidian regime (f<f_{cN}),
where it is determined by the commensurability of the vortex lattice with the
effective potential created by the array. Anomalies observed in both the
periodicity and the symmetry of L(f) are attributed to the effect of a hidden
incommensurability, which arises from the deformation of the magnetic field
distribution caused by the asymmetric diamagnetic response of the
superconducting islands forming the arrays.
