An Inspiration of The Mandelbrot Set

Pantea Ferdosian

Dr. Sander

December 6, 2019

An Inspiration of The Mandelbrot Set

What does the Mandelbrot Set represent?

In the purest sense, the Mandelbrot set is simply a set of numbers that display certain unusual property, but since the set is always associated with an image that represents this property, we often use the term “Mandlebrot Set” to describe the image itself. The Mandlebrot set is a visual representation of an iterated function on the complex plane. 

The Mandelbrot set is a set of all numbers that DO NOT grow exponentially in the iterated function  and are typically represented by the color black. If we have a black circle, an image of the complex plane that shows all the possible numbers in the Mandelbrot set displayed in black, and iterate the function , each time in a different color, infinitely many times, we would end up with this shape:

For my specific print, as shown in the code, I manipulated my function for Manderlot set a bit to show how it would still be similar to the initial function. I raised my function to the power of 0.9.

But I also raised it to 2,3,4, and 5 and got very cool illustrative results: