The Mandelbrot set

This applet draws the Mandelbrot set, i.e. the set of points

of the complex plane for which the orbit of

under the iteration map

is bounded, that is, it does not "escape to infinity". It can be shown that the Mandelbrot set corresponds to the set of points

for which the corresponding Julia set is connected (i.e. it is not the union of disjoint open subsets).

Use the Draw button to start rendering the set and the Clear button to (stop and) clear the window.

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