Which Perlin noise is the best?

When one says "Perlin Noise" it's not clear which version of the noise function you mean.   Even using it inthe strict sense of which noise Ken Perlin described is not enough-- he has modified it in a later siggraph paper!

I asked Andrew Kensler at Pixar what noise I should use because he knows the most about noise of anybody in my extended ecosystem.   It turns out Andrew has an awesome tool for looking at the Perlin variants and a pointer to other work to help decide for yourself, as well as the best description of noise I am aware of.   It's part of his newwish blog I hope we will see a lot of.   Here's a screen shot of the setting for the original Perlin noise so you can visually compare as you play with variants: