Function Playground
Graph any function on the real line, drag the point around, then flip to the complex plane and watch the same function warp it with color.
What is happening here?
Real graph is the familiar picture: the curve y = f(x), a draggable dot, and the tangent line at that dot. The tangent's slope is the derivative — the same slope Newton's method uses to take its steps.
Complex plane feeds every point z of the plane through f and paints the result: the color's hue is the answer's angle, and the rings mark each doubling of its size. Drag z across the dark seam under √z to feel the branch cut — the answer jumps from +i to −i.
f(x) =
click or drag on the graph to move x · dashed line is the tangent at x