The Universe in Colour: Mandelbrot Set

A new feature! Each week I’ll post an image related to something from Physics, Philosophy or Mathematics and say a little bit about it and it’s significance.

The Mandelbrot Set

Let’s start off with a version of the mathematical image I selected as the logo for this blog:

Image result for mandelbrot
Mandelbrot Set

Nothing quite exemplifies the beauty of mathematics as the Mandelbrot Set. The image above is a kind of fractal. A fractal is a shape that looks exactly the same no matter how much you zoom in or out out of it. I would strongly recommend watching a video that simply zooms in on a Mandelbrot Set, it’s awe-inspiring!

Despite its visually complex structure, a Mandelbrot set is mathematically very simple to construct!

The Mandelbrot set is the set of complex numbers c for which the function

{\displaystyle f_{c}(z)=z^{2}+c}

does not diverge when iterated from z=0. What is meant by this is: pick any complex number c. Then starting with z=0, keep applying that function. If the result of applying this function just gets larger and larger, then the point representing this number on the image is coloured based on how quickly it diverges. Otherwise, the point is coloured black and the number represented by that point is in the Mandelbrot Set.

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