See what a complex function does to the plane.
Type f(z) and every point of the complex plane gets colored by where it lands: hue shows
the phase (argument) of f(z), brightness shows its magnitude, with rings marking each
doubling in size. Pan and zoom in real time. For the rational-function presets, poles and zeros are
marked exactly, using the same root finder as the rest of the site. Runs in a WebGL shader when your
browser supports it, with an automatic slower fallback when it doesn't — either way, nothing leaves
your browser, and every expression still goes through the same whitelisted parser with no eval.
Click anywhere on the plot to inspect that point.
Still no eval, ever
f(z) is parsed by the exact same tokenizer → parser → whitelist as every other tool here. The only new step is a second, typed code generator that turns that same validated tree into a GLSL shader — nothing about the "never eval" guarantee changes.
Scoped on purpose
Functions without a well-defined complex meaning (asin, sinh, floor, atan2, mod, min/max, and the pow(...) form) are only allowed on real-valued sub-expressions, with a clear message if you try otherwise — rather than silently guessing at a generalization.
Bounded by design
Zoom is capped before it hits float32's precision wall, the no-WebGL fallback renderer caps its resolution so it can't hang your browser, and poles/zeros are only ever shown for presets whose exact coefficients are known — never guessed from arbitrary typed input.