Indexing the archive…
Your Universe of Digital Possibilities
This is not a picture of a fluid; it is a fluid. Every frame solves the incompressible Navier–Stokes equations on a grid — advection, viscous diffusion, and a pressure projection that forbids the fluid from compressing. Drag across the tank to inject motion and dye; thin the viscosity and stir harder to push smooth, layered flow over the edge into turbulence — the regime no one has yet proven stays smooth.
The whole of classical fluid motion in two lines: a parcel accelerates from pressure gradients, viscous drag (ν∇²u) and any body force f. The constraint ∇·u = 0 says an incompressible fluid can swirl freely but never pile up.
Stam’s insight: don’t step the velocity forward (which blows up), trace it backward — ask where each parcel came from and copy that value. This semi-Lagrangian advection is unconditionally stable, which is why it runs in real time in your browser.
Any vector field splits (Helmholtz) into a divergence-free flow plus the gradient of a scalar. We solve a Poisson equation ∇²p = ∇·u* for that scalar and subtract its gradient, leaving a mass-conserving field. This is the projection step every frame.
One dimensionless number decides everything: the ratio of inertia to viscosity. Low Re, the fluid moves in smooth sheets; past a critical value (~2000 in a pipe) it shatters into eddies on every scale. The readout above is this number, in the instrument’s own units.
The old Field on this rack faked a flow with folded sine waves; this one solves the real equations, and they bite back. Turbulence is spatiotemporal chaos — the same sensitivity to initial conditions that The Divergence and The Attractor show in a few variables, now spread across a whole field at once. And there is a deeper humility here: we can integrate Navier–Stokes forward faster than thirty times a second, yet no one has proven that its three-dimensional solutions always stay smooth — that they never blow up to infinite speed from a calm start. That proof is a Clay Millennium Problem, still unclaimed. You are stirring a machine humanity can run but cannot fully understand.