Curl-noise for procedural fluid flow

Procedural methods for animating turbulent fluid are often preferred over simulation, both for speed and for the degree of animator control. We offer an extremely simple approach to efficiently generating turbulent velocity fields based on Perlin noise, with a formula that is exactly incompressible (necessary for the characteristic look of everyday fluids), exactly respects solid boundaries (not allowing fluid to flow through arbitrarily-specified surfaces), and whose amplitude can be modulated in space as desired. In addition, we demonstrate how to combine this with procedural primitives for flow around moving rigid objects, vortices, etc.