Experimental discovery of scaling laws relating fractal dimensions and the length distribution exponent of fault systems

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 remarquable 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.