  Two different multi-resolution analyses are used to decompose the structure
of active region magnetic flux into concentrations of different size scales.
Lines separating these opposite polarity regions of flux at each size scale are
found. These lines are used as a mask on a map of the magnetic field gradient
to sample the local gradient between opposite polarity regions of given scale
sizes. It is shown that the maximum, average and standard deviation of the
magnetic flux gradient for alpha, beta, beta-gamma and beta-gamma-delta active
regions increase in the order listed, and that the order is maintained over all
length-scales. This study demonstrates that, on average, the Mt. Wilson
classification encodes the notion of activity over all length-scales in the
active region, and not just those length-scales at which the strongest flux
gradients are found. Further, it is also shown that the average gradients in
the field, and the average length-scale at which they occur, also increase in
the same order. Finally, there are significant differences in the gradient
distribution, between flaring and non-flaring active regions, which are
maintained over all length-scales. It is also shown that the average gradient
content of active regions that have large flares (GOES class 'M' and above) is
larger than that for active regions containing flares of all flare sizes; this
difference is also maintained at all length-scales.
