Vector Field Visualizer
Enter the two components of a vector field and see it come alive as a quiver plot, colored and scaled by magnitude. Explore rotations, sources, saddles, and spirals.
Vector Field StudioLive
F(x,y) = (u, v) · quiver plot · drag to trace a flow line
Controls
Data Inspector
Arrows374
Domain[-5,5]²
Probe(2.5, 0.0)
Governing equation
Reading this result: A pure rotation field: every arrow is perpendicular to the radius, so the flow circles the origin with zero divergence and constant curl.
Runs locally in your browser — free forever. Scale to the cloud when reality gets heavy.
★ Sign in to save this setupSave your tuned setup, or drop this simulation into your own site, docs, or course page.
How it works
Both components are parsed by PolySim's symbolic engine and evaluated across a grid of (x, y) points. Each arrow points along the field direction and is scaled and colored by magnitude — the standard way to visualize flow fields, force fields, and the phase space of 2D dynamical systems.
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The math, the assumptions, real-world uses, or a code translation — explained for this exact simulation.
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Frequently asked questions
Is this vector field visualization tool really free?▾
Yes. Vector Field Visualizer runs entirely in your browser using your device's own compute, so local use is free forever. You only pay Compute Tokens if you scale a job to the cloud.
Do I need to install anything?▾
No. Everything runs client-side in a modern browser — no downloads, no license, no account required to start.
Can I save or share my simulation?▾
Create a free account to save projects, and use a shareable embed or minted DOI to publish a live, interactive version anywhere.
How accurate are the results?▾
The solver uses established numerical methods, but results are for research and educational purposes and should be validated against experiment or professional review before you rely on them.