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Here's a good one: (e*r)^(e*r)/(abs(e^(e*r)-(e*r)^(e))+0.05)+0.15/r^3. At close distances, it acts like 1/r^3. But as you head out, gravity suddenly increases, maxing out at r=1. Head even further out and gravity decreases, then increases in proportion to e^(r*ln(r))=r^r, which is between exponential and double exponential.

Watch this at 1x:
Notice that the planets start out in nice circular orbits, then chaos causes the inner ones to suddenly (and repeatedly) plunge into the triple suns, coming out on random looking trajectories. The outer planet (which has a shorter orbital period) eventually collides with them and ends up on a stable, flowerlike orbit.

Huh, that's cool how the outermost planet really just keeps doing its own thing. All the other ones flew around pretty chaotically, but that one just kept circling and circling (with minor wobbles here and there). I suppose it just had too much kinetic energy to get pulled any closer to the center, maybe? (I was surprised to see another planet cross the stable planet's path...so it's not just it's position that keeps it safe, conservation of angular momentum must come into play)

sin(4*(log(r)/log(1.6)))/(r^3) produces star shaped orbits.
I found that it's possible for a moon to orbit a planet using this law.