Especially nice considering how often the "fingers" get in the way of fractals like that (and if you increase the bailout to try to reduce that effect, you start getting moire effects, and eventually end up with Cantor dust since it's "fingers all the way down").
For a good introduction to the "BRD" set (and some other pretty pictures), check out:"Growth in Complex Exponential Dynamics"
Hi Gandreas, thanks a lot for the link.
Actually, my formula is much friendlier than those in the article, like f(z) = lambda * exp(z). In my formula, if z is large, the formula is about like f(z) = z * exp(-1/(p*c)), which, assuming Re(c) > 0, makes z smaller; and if z is small, the formula is about like f(z) = z * exp(1/p), which makes z larger.
I said that my images are characteristic of the dynamics of functions with complex exponentials, but perhaps I should restrain my words. One thing I found characteristic of a certain class of formulas are the points where we see an infinite number of branches originating, and with a clear-cut separation along a line. These singularities appear because of the poles of the function w = (1-z^p)/(p*(1+c*z^p)); near the pole, w will be very large in absolute value, either with real part positive or negative, and thus exp(w) will be either very small or very large.
My images were still a challenge regarding anti-aliasing. I found that sometimes I needed 16x16 supersampling to get adequate results.