This tool graphs a function f(z) on the complex plane. The color hue represents the angle, and the brightness represents the magnitude of the output value. Enable level curves to graph only the fractional part of the magnitude, which produces sharp curved lines at every integer increment. Use the output scale to multiply by a factor if you need to bring the colors or curves into a more interesting range for the function. You can also copy a URL of your graph to embed on other websites in an <iframe> element.

The function box accepts math expressions and C-like programs. You can write loops to perform summations and fractal iterations. The following code structures are available (click on the examples above to see how to use them):

Run code only if an expression is true.
Use an else block to run different code otherwise.
if (...expression...) { ...code... }
else { ...code... }

Define a complex variable, and assign a value.
complex a = ...expression...;

Return a value immediately, skipping all future code.
return ...expression...;

Loop the integer n over the range [start, end-1]
You can use n as a variable inside the loop.
loop (n, start, end) { ...code... }

Continue to the next loop increment immediately.
loop (n, start, end) { continue; }

Exit the loop immediately.
loop (n, start, end) { break; }

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Graph Controls:

With a mouse, click and drag to pan. Hold Alt or use the scroll wheel to zoom.

With a touchscreen, touch and drag with one finger to pan. Pinch with two fingers to zoom.

With a keyboard, use Ctrl+[Arrow Keys] to pan. Use Ctrl+< to zoom out, and Ctrl+> to zoom in.