Complex functions live in four dimensions — domain coloring squeezes them onto the plane so you can actually see them. Hue is phase; brightness is magnitude.
Complex Function VisualizerLive
domain coloring · f(z) on the complex plane
Controls
Domain coloring maps each complex output to a color: hue = phase (argument), brightness = magnitude. Zeros are dark, poles are bright.
Reading this result: z² doubles every angle, so the hue wheel wraps twice around the single zero at the origin — a double root shows as two full color cycles.
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
Every point of the complex plane is colored by the output of f(z): the hue encodes the argument (phase) and the brightness encodes the magnitude. Zeros appear as dark points and poles as bright ones, making the structure of functions like 1/z and (z²−1)/(z²+1) immediately visible.
✦
Ask the AI about this model
The math, the assumptions, real-world uses, or a code translation — explained for this exact simulation.
Is this complex function visualization tool really free?▾
Yes. Complex Function 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.