Mandelbrot set

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The Mandelbrot set is the set of complex numbers c
for which the function fc(z)=z^2+c
does not diverge when iterated from z=0, i.e.,
for which the sequence fc(0), fc(fc(0)), etc.,
remains bounded in absolute value.

Its definition is credited to Adrien Douady
who named it in tribute to
the mathematician Benoit Mandelbrot,
a pioneer of fractal geometry.[1]