The swollen lamellar phase Lα and the anomalous isotropic phase L3 (sponge) are presently the only two dilute phases of fluid membranes in amphiphilic systems that have been clearly characterized. We here deal with the L3 phase. We first recall the scale invariance argument leading to the φ3 scaling law for the free energy density of phases of fluid membranes. We extend it further in order to derive scaling laws for several static and dynamic physical properties of L3. The effects of renormalizations of the membrane area and of its elastic constants with scale length scattering, electric birefringence and flow birefringence. The results obtained are puzzling since static quantities exhibit logarithmic corrections due to renormalizations while dynamic ones do not