Taking the curl of a noise field will get you a divergence free flow field[1]... which is an easy way to get something that <i>looks</i> like fluid dynamics, but isn't.<p>I've use this to great effect on the surface of a sphere to generate textures for gas giants[2]. Some example output: <a href="https://imgur.com/a/9LipP" rel="nofollow">https://imgur.com/a/9LipP</a><p>1. <a href="https://www.cs.ubc.ca/~rbridson/docs/bridson-siggraph2007-curlnoise.pdf" rel="nofollow">https://www.cs.ubc.ca/~rbridson/docs/bridson-siggraph2007-cu...</a>
2. <a href="https://github.com/smcameron/gaseous-giganticus" rel="nofollow">https://github.com/smcameron/gaseous-giganticus</a>
I think it would be interesting to add a z dimension so you could sweep through it with the plane to look for the best aesthetic in the field. Kind of like passing a line laser through smoke. You could even slice along a spline or some other function (e.g. spiral) to get more effects.<p><a href="https://www.youtube.com/watch?v=iyhySKWPtmA" rel="nofollow">https://www.youtube.com/watch?v=iyhySKWPtmA</a>
Really cool explanation! Some of the generated forms remind me if Julie Mehretu stuff: <a href="https://www.artsy.net/artist/julie-mehretu" rel="nofollow">https://www.artsy.net/artist/julie-mehretu</a>
This can be generalized to scalar and vector fields in any number of dimensions. These things are everywhere in generative art. The discretization done by the author here is often not necessary, though.<p>The graphical programming environment vvvv has a pack of nodes ("field trip") for manipulating these in 2D and 3D. Fun to play with, and it's been used to create many beautiful pieces.
Flow fields are also great for reducing the amount of computation required to generate pathfinding for a large number of entities in a game world. I implemented flow fields as the pathfinding for the enemies in a game I was working on last year and it works really well.