Simulation noise

Simulation noise is a function that creates a divergence-free field. This signal can be used in artistic simulations for the purposes of increasing the perception of extra detail.

The function can be calculated by dividing the space into a regular lattice grid. With each edge is associated a random value, indicating a rotational component of material revolving around the edge. By following these rotations into and out of faces, one can quickly sum the flux coming in and out of each face of the lattice. Flux values at lattice faces are then interpolated to create a field value for all positions in the lattice cube.

Perlin Noise is the earliest form of lattice noise, which has become very popular in computer graphics. Lattice noises at difference frequencies are often summed together to form fractal signals. Perlin Noise is not suited for simulation because it is not divergence-free.