Mandelbrot set

Iterate z² + c on the complex plane — the boundary is infinitely jagged.

Take a complex number c. Repeatedly compute z → z² + c, starting from z = 0. The set of c for which z stays bounded is the Mandelbrot set.

Try this

c (real part, as c = slider ÷ 10)

-5

z → z²+c after 40 steps: = stays bounded — c IS in the Mandelbrot set

Its boundary is infinitely detailed — fractal. Zoom in forever, and new structure keeps appearing.