Flow Fields — Image Pack

A flow field assigns to every point in the plane a direction — and a particle dropped into the field will trace a curve that always follows the local arrow. Build the field from smoothly varying noise (Perlin, simplex, or layered sinusoids) and the resulting trajectories braid into curtains, vortices, and rivers without ever crossing. The technique sits at the boundary of generative art and computational fluid dynamics. Each image in this collection is the result of thousands of particles released into a fixed mathematical field, each one rendered as a continuous trail. The animations show the same fields evolving slowly in time, so that the entire flow pattern breathes while maintaining its underlying structure.

∂x/∂t = cos(N(x,y)), ∂y/∂t = sin(N(x,y)), N = Σ aₖ sin(fₖ·r + φₖ)