Mandelbrot Set

The Mandelbrot set is an impressive example of a complex structure arising from simple rules. It is named after Benoit Mandelbrot who made significant contributions to fractal geometry [1]. The set represents the convergence set of the sequence \begin{align} \begin{split} z_{n+1} = z_n^2 + c \end{split} \end{align} as a function of the complex number \(c\).

To zoom into the set click and drag to select a rectangle. At any point you can return to the initial view with right click of the mouse.

References

  1. Benoit Mandelbrot (1980). Fractal aspects of the iteration of \(z \to \lambda z ( 1 − z )\) for complex \(\lambda\) , \(z\). Annals of the New York Academy of Sciences, 357, 249–259. ↩