Julia Sets

The Mandelbrot set’s family

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

• Fix $c$, vary the starting point: the Julia set is the boundary between bounded and escaping points.
• c in the Mandelbrot set ⇔ its Julia set is connected; outside, it is dust.
• $z^2$ gives a circle, $z^2 - 2$ an interval, and other values of $c$ give fractals.

Steps

1. The simplest case
2. Choose your c
3. A dictionary
4. A gallery
5. A short cycle
6. The interval