  We study the electronic energy spectra and wave functions on the square
Fibonacci tiling, using an off-diagonal tight-binding model, in order to
determine the exact nature of the transitions between different spectral
behaviors, as well as the scaling of the total bandwidth as it becomes finite.
The macroscopic degeneracy of certain energy values in the spectrum is invoked
as a possible mechanism for the emergence of extended electronic Bloch wave
functions as the dimension changes from one to two.
