  The ability to transmit light through an array of closely packed waveguides
while minimizing interwaveguide coupling has important implications for fields
such as discrete imaging and telecommunications. Proposals for achieving these
effects have leveraged phenomena ranging from Floquet-induced flat bands to
Anderson localization. Here we demonstrate that, for strongly detuned
waveguides, optimal localization is achieved not by disorder but by fractal
potentials. We further show that, in both 1D and 2D, these structures possess a
localization-delocalization phase transition.
