  The tight-binding model for a chain, where the hopping constants follow a
Fibonacci sequence, predicts multifractality in the spectrum and wavefunctions.
Experimentally, we realize this model by chains of small dielectric resonators
with high refractive index ($\epsilon_r \approx 45$) of cylindrical form that
exhibit evanescent coupling. We show that the fractality of the measured local
density of state (LDOS) is best understood when the sites are rearranged
according to the similarities in their local surrounding, i.e., their
conumbers. This allows us to deduce simple recursive construction schemes for
the LDOS for the two cases of dominant strong and weak coupling, despite our
limited resolution due to non-zero resonance width and size constraints. We
measure the singularity spectrum and the fractal dimensions of the
wavefunctions and find good agreement with theoretical predictions for the
multifractality based on a perturbative description in the quasiperiodic limit.
