Posted by Jason Polak on 13. June 2013 · Write a comment · Categories: analysis, elementary · Tags: , ,

A class of fractals known as Mandelbrot sets, named after Benoit Mandelbrot, have pervaded popular culture and are now controlling us. Well, perhaps not quite, but have you ever wondered how they are drawn? Here is an approximation of one:

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From now on, Mandelbrot set will refer to the following set: for any complex number $ c$, consider the function $ f:\mathbb{C}\to\mathbb{C}$ defined by $ f_c(z) = z^2 + c$. We define the Mandelbrot set to be the set of complex numbers $ c\in\mathbb{C}$ such that the sequence of numbers $ f_c(0), f_c(f_c(0)),f_c(f_c(f_c(0))),\dots$ is bounded.
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