The electronic properties of a tight-binding model which possesses two types of hopping matrix element (or on-site energy) arranged in a Fibonacci sequence are studied. The wave functions are either self-similar (fractal) or chaotic and show "critical" (or "exotic") behavior. Scaling analysis for the self-similar wave functions at the center of the band and also at the edge of the band is performed. The energy spectrum is a Cantor set with zero Lebesque measure. The density of states is singularly concentrated with an index ae which takes a value in the range [cte'", az'"]. The fractal dimensions f(ae) of these singularities in the Cantor set are calculated. This function f(ae) represents the global scaling properties of the Cantor-set spectrum.