We analyse various properties of the visibility diagrams that can be used i
n the context of modular symmetries and confront them with some recent expe
rimental developments in the quantum Hall effect. We show that a suitable p
hysical interpretation of the visibility diagrams, which permits one to des
cribe successfully the observed architecture of the quantum Hall states, gi
ves rise naturally to a stripe structure reproducing some of the experiment
al features that have been observed in the study of the quantum fluctuation
s of Hall conductance. Furthermore, we show new properties of the visibilit
y diagrams stemming from the structure of subgroups of the full modular gro
up.