The long-time behaviour (t greater than or equal to 1 ms) of dipolar couple
d nuclear spin systems, highlighted by the high resolution nuclear magnetic
resonance (NMR) spectra of abundant nuclei in rigid solids, is explained s
atisfactorily as a manifestation in NMR of the famous 'long-time tail effec
t'. The time dependence of the transverse magnetization at the long-time li
mit, which is fundamentally different from the initial exponential decay, i
s closely related to the dimension of the spin network embedded in real spa
ce, opening a new approach to measuring the fractal dimension of coupled sp
ins in solids.