Basically what the recursion does it looks at the local curvature and decides if the line drawn is 'good' enough or needs refinement, if so, the lines is divided in two.

So what maxrecursion -> 15 means, is that between 2 plotpoint is should be (at most) be divided up to 2^15 = 32000 times!! This is not what you want to use maxrecursion for.

You want to use maxrecursion if your function shows generally very smooth behavior but only at some point a very 'curvy' behavior, so that can be corrected there. If your function is generally curvy everywhere, it is better to increase plotpoints, and put maxrecursion to 2 or 3 or so (low value). To be honest, I've never (in 12-13 years or so) i've never used (or seen used) maxrecursion higher than 4. That basically means that function is 16x more curvy at some particular point than the rest. Of course this could happen, but very unlikely I would say!

Thanks Michael. Yes, increasing PlotPoints helps quite a bit. I've been looking for the optimal combination of PlotPoints and MaxRecursion to maximize detail and minimize computation time. I thought it would be useful to try raising MaxRecursion even higher, since large PlotPoints takes a long time as well. If anyone knows of a way raise the MaxRecursion limit, please post :)