Mandelbrot Set

Explore an Infinite Mathematical Universe

The Mandelbrot set is a region of the complex plane with an infinitely complex boundary. Zoom into any point on its edge and discover endlessly repeating structures — spirals, miniature copies, and alien coastlines.

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What is the Mandelbrot Set?

z_{n+1} = z_n^2 + c

For each point $c$ in the complex plane, start with $z_0 = 0$ and repeatedly compute $z_{n+1} = z_n^2 + c$ . If never exceeds 2, the point is inside the set. The boundary between points that escape and those that do not is infinitely complex: a fractal coastline with no end.