Flux quantization on quasicrystalline networks

We have measured the superconducting transition temperature Tc(H) as a function of magnetic field for a network of thin aluminum wires arranged in two quasicrystalline arrays, a Fibonacci sequence and the eightfold-symmetric version of a Penrose tiling. The quasicrystals have two periods whose ratio is irrational and are constructed of two tiles with irrationally related areas. We find a series of dips in Tc(H) corresponding to favorable arrangements of the flux lattice on the quasi-crystalline substrate. The largest dips are found at n and the dips approach the zero-field transition temperature as n increases.