Are granitic intrusions scale invariant?

Published length (L) and thickness (T) data on 135 laccolith and 21 granite intrusions define power-law relationships of the form L = kT(a) typical of systems exhibiting scale invariant (fractal) behaviour. Both data sets are characterised by an exponent a < 1 (0.88 +/- 0.1 for laccoliths and 0.80 +/- 0.20 for plutons) that reflects an inherent preference for scale invariant tabular-sheet geometries. These power-law size relationships can be explained in mechanical terms by the need for an incoming magma sheet to travel laterally some distance before vertical thickening can occur. Sheet thickness is a function of available magma pressure which for an intrusion fed by a feeder dyke is proportional to the vertical magma transport distance.