A series of experiments scaled for gravity on the formation of faults in a laboratory model of the earth's lithosphere have shown that the obtained fault patterns are self-similar and can be characterized by various fractal dimensions. By analyzing a large set of experimental results, we discover a remarkable scaling law relating the generalized fractal dimensions Dq, the fault barycenter fractal dimension 'b' and the exponent 'a' of the fault length distribution. : D0=b is independent of 'a' whereas Dq≥1=b+2-a, for 2≤a≤3 as found in our experiments. ¿ American Geophysical Union 1992