Picture every point on the screen carrying a hidden arrow that says "go this way." Assign that angle purely at random per pixel and you get static; assign it with a smoothly-varying noise function instead and neighbouring angles stay close, so particles trace flowing, water-like curves.
Each frame, every particle reads the field angle at its own position, steps one unit in that direction, and leaves a thin line behind. Instead of clearing the canvas each frame, the demo paints a barely-visible translucent rectangle over it first — old trails fade instead of vanishing, which is what produces the streaked, painterly look.
Designers reach for this for poster backgrounds, album art and loading screens — anywhere that needs a texture that feels organic but still obviously rule-based. Changing the scale of the underlying noise trades a loose, sweeping flow for a tight, swirling one.
When to use
Use it when a plain gradient feels too static. Tune particle count and trail opacity to control density.