Fractal Flower

This is a visual representation of the Mandelbrot set. Each pixel in this 2d graph represents a number c with an imaginary component (yi) and a real component (x), c= x+yi.

They are colored white or black depending on if the recursive series shown below diverges to infinity for a given c. Each element in this series is determined by recursive application of the following function: f(z) = z^n +c, where the intial value of z is set to 0.

f(0) = 0^n + c
f(f(0)) = c^n + c
f(f(0)) = (c^n+c) ^n +c
…. and so on onto infinity.

If the series f(0), f(f(0)), f(f(f(0))) … does not increase into infinity, then the pixel associated with the number c is colored white. Else it is colored black. In this animation, I increase the power n from 0.1 to 10 to generate the additional “petals”.

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