Sorry, I meant square, not square root. I kept trying your idea with poor results, and then I tried square-root with results that had no resemblance to what I'd done before. Finally, I had the good sense to sit down with my beloved HP-48 and think about what the exponents did.

Exponents greater than one tend to flatten low areas and sharpen high areas. Exponents less than one tend to sharpen low areas and round off the peaks. An exponent of one tends(perfectly) to leave everything as is. Oh, yeah, if you want a cueball planet, an exponent of zero is perfect .