Mathematics

Mandelbrot & Julia Sets

Two views of one complex-dynamical system—and a direct path from equation to image.

01

One rule, two perspectives

Both families use z → z² + c. The Mandelbrot set varies c to map the behavior of the entire family. A Julia set fixes one c and reveals the detailed world associated with that coordinate.

02

From orbit to color

Each screen pixel becomes a complex coordinate. The app iterates the formula, measures escape behavior, then sends the result through a precision color pipeline. The image is not stored artwork; it is computed for the view you chose.