The Mandelbrot Set

Infinite complexity from z² + c

An interactive lesson with 6 steps, about 5 minutes: you predict, drag and solve, with instant feedback on every answer. It runs in your browser and needs JavaScript.

What you’ll learn

• Mandelbrot set: the values $c$ for which $z \to z^2 + c$ (starting from 0) stays bounded.
• If $|z|$ ever exceeds 2, the sequence escapes.
• Its boundary has endless detail, with tiny copies of the whole set.

Steps

1. A simple rule
2. In or out?
3. Zoom in
4. How fast does it escape?
5. Area and edge
6. Escape test