Fractal Dimensions, Flares, and Forecasts

FIGURE 1: The y axis is 'at least one flare of this size per day', and the x axis is the fractal dimension. Hence a minimum fd=1.2 is needed to get an M-flare, a minimum fd=1.25 is needed for an X-flare

FIGURE 2: This figure is figure 1 binned over fractal dimension. The coloring indicates the number of flares of least size Y produced by an active region of fractal dimension X. As Jack pointed out, anything can be plotted on the x axis - the only requirement is that is quantifiable and automated. All we have really done is automatically quantifed complexity with fractal dimension. NB: the intensity colouring is on a log scale.

FIGURE 3: By plotting normalised vertical cuts through Figure 2, it is possible to get flare predictions for each value of fractal dimension.
A fractal dimension of 1--1.05 gives a 90% chance of no flares.

A fractal dimension of 1.2--1.25 gives a 15% chance of a c-class activity, and 5% chance of M-class activity

A fractal dimension of 1.3--1.35 gives a 20% chance of a c-class activity, and 5% chance of M-class activity

A fractal dimension of 1.4--1.45 gives a 30% chance of a c-class activity, and 10% chance of M-class activity
Because there so few x-flares (total of only 42, compared to 429 M-flares, 3152 C-flares), the probabilities for X-class flares are always small, barely ever getting above 1% for any bin. It is also important to note that of the 10,000 active regions studied, 7500 did not produce any flares - hence the need to plot figure 2 on a log intensity scale - so that even at large fractal dimension 2/3 of regions produced no flare.

And of course I can make these plots for any fractal dimension and for any fractal dimension bin size. Probably a binsize of 0.05 is sensible, as the error in any value is 0.02--0.03.

ADDITION: I'm only taking regions at less than 60 degrees from disc centre. So I'm missing out on limb flares, but I don't see how this could bias the results

Obviously the figures need more work but the general idea is there. Comments?