Electronic spectrum of the two-dimensional Fibonacci lattice

The electron spectrum and wave functions of the two-dimensional Fibonacci lattice with “central” and “vertex” decorations are considered. The energy spectrum contains a singular part but does not contain a hierarchical gap structure. The measure of permittable states of the spectrum (the Lebesgue measure) is not equal to zero and in the case of central decoration is close to unity. Most of the wave functions are critical.