This is Jos Stam's classic "stable fluids" method, the same trick behind most real-time smoke and ink demos. Two textures ping-pong every frame: a coarse velocity field that drives the motion, and a separate, higher-resolution dye field that just rides along for the picture — which is why the colors look far more detailed than the underlying simulation grid. Each step advects both fields along themselves (semi-Lagrangian: it traces every cell backwards through the flow, which stays stable at any frame rate instead of blowing up), re-injects some of the curl that numerical diffusion quietly smooths away so eddies stay lively (vorticity confinement), then projects the velocity back to zero divergence by solving a discrete pressure Poisson equation with a couple dozen Jacobi relaxation passes and subtracting its gradient — the step that keeps the fluid incompressible, so nothing appears or vanishes anywhere on the grid. Switch the brush to Wall to paint solid obstacles the flow curls and splits around (Erase wall to remove them again, Clear walls to wipe the lot — plain Clear only resets the dye and motion); walls live on their own fine-grained grid, so their edges stay crisp and your drawing survives unchanged whatever the Sim res slider says. Use PNG or Record GIF to save a still image or a short looping clip of whatever you've made.