  We study the critical depinning current Jc versus the applied magnetic flux
Phi, for quasiperiodic (QP) chains and 2D arrays of pinning centers placed on
the nodes of a five-fold Penrose lattice. In QP chains, the peaks in Jc(Phi)
are determined by a sequence of harmonics of the long and short segments of the
chain. The critical current Jc(Phi) has a remarkable self-similarity. In 2D QP
pinning arrays, we predict analytically and numerically the main features of
Jc(Phi), and demonstrate that the Penrose lattice of pinning sites provides an
enormous enhancement of Jc(Phi), even compared to triangular and random pinning
site arrays. This huge increase in Jc(Phi) could be useful for applications.
