The picture looks calm.
The peak is missing.
A computer checks points. Intense motion can hide between them.
Reveal the blind spot. See what extra detail recovers.
A hands-on lesson in why a reassuring picture is not enough to trust a calculation.
Try the revealA small region.
A very big extreme.
In the announced construction, the core holds less energy as its characteristic speed grows. Here is one comparison using the paper’s scales:
OpenAI’s announced proof constructs a specially forced flow that starts smoothly and develops unbounded speed in finite time, while its total energy stays finite. A bound on total energy does not guarantee a bound on local speed.
The experiment above makes a related numerical lesson visible: a coarse grid can miss a tiny peak. We use a separate vortex with a known answer, so you can measure the error and see how local detail improves the estimate.
The useful habit is to check what your calculation can resolve before trusting its picture. Grid refinement already existed. This experiment illustrates the lesson; it does not reproduce the singularity or establish that an engineering design is safe.
Read OpenAI’s announcementWhy care about getting flow right?
Because we use these equations to understand the places we live and the things we build. Explore three familiar examples in the same live airflow playground.
Why is it so windy between buildings?
Bring the buildings closer together. Watch the flow squeeze through the gap—and feel the difference at the marker.
Change something small. Watch the flow change around it.
Look inside the mathematical discoveryThe shrinking-core microscope
How can a tiny region move faster while carrying less energy? It contains less and less fluid. The original microscope lets you explore the paper’s characteristic core scales.
Try the computer’s blind spotCan a coarse grid see a tiny vortex?
Inspect the same sampling benchmark from above in a flat view, compare all three grids, and download its measurements. The focused patch is deliberately placed at the known center.
What is actually being simulated?Methods, sources, and limits
The everyday scenes run a live two-dimensional lattice-Boltzmann model in your browser. It approximates incompressible Navier–Stokes flow at low speed, using a 192 × 104 lattice, viscosity 0.03 in lattice units, a fixed inlet speed of 0.032, a fixed-density outlet, periodic top/bottom edges, and no-slip solid boundaries.
The street is an idealized channel between two solid blocks, the windbreak is a solid barrier, and the leading rider is an ellipse. Buildings have no simulated height. The marker is a passive probe, not another solid person, chair, or cyclist. Its reading averages speed over nine nearby cells and divides by the incoming speed. It does not predict cycling effort, gust safety, building loads, or weather. Animation time is illustrative; the calculation evolves in lattice time steps.
The live field can develop and fluctuate. After changing geometry, wait for the flow to develop. Dragging a marker through an existing field gives an immediate comparison. The color overlay highlights faster and slower regions using the same incoming-flow reference.
The main reveal and optional flat grid view sample static Lamb–Oseen vortices with unit peak speed. Their sliders choose independent snapshots; they do not integrate a fluid in time. The raised plot uses height and color for speed, with fixed view bounds and shared scales. Its surface interpolates the sampled values for display; the metrics use the underlying point evaluations. Its coarse grid uses 256 evaluations, its known-center patch uses 1,280 including overlap, and its uniformly fine grid uses 16,384. It measures peak sampling error, not overall solver accuracy. The optional microscope and the core comparison above use the paper’s core scaling at h = 0.005; its 3D particles are schematic. Neither experiment recreates the complete announced proof.