I discovered last year these tutorials by Jasper Flick on how to make and use noise in Unity, and a couple of terrain and particle use examples. They present the difference between value noise and gradient noise, how Perlin noise and simplex noise work, and among others how to use curl noise to control the flow of particles.

The order information is presented is well thought, although the intention might not be clear at first. Don’t let the beginner’s tutorial tone (“You’ll learn to: create and fill a texture;”, etc.) turn you away, as the series do a great job at detailing the concepts and algorithms in a simple manner yet without cutting corners like so many articles on the topic do (when they’re not blatantly wrong and go ahead calling a blurred noise “Perlin noise”). I thought I had a pretty good grasp of gradient noise already, but reading it gave me an even better understanding.

• Noise
• Noise Derivatives
• Simplex Noise

Pushing particles around with Simplex curl noise.

While at it, other resources on the topic include Ken Perlin’s GDC 1999 talk and his two pages paper Improving noise explaining why use a 5th order polynomial for interpolation (a function I’ve sometimes seen called “smootherStep”).