Maths Town (title)
Maths Town (title)


This video is a demonstration of what happens when you increase the power of the Mandelbrot Set.  The associated equation is in the lower right hand corner of the video.  Integer powers give the family group of Mandelbrot shapes and are analytic.  Non-integer powers are non-analytic and are full of fault lines.

We start with the classic and most famous Mandelbrot Fractal (n=2) then move to the higher powers of n. From n=2..10 we go quite slowly, then we speed up and accelerate quickly from n=10..100. You will start to see that as n approaches infinity the Mandelbrot fractal becomes a circle (of radius 1).

 

 

 

Software

The series of images that made this video were rendered with Ultra Fractal.

 

 Image Gallery

Note: The video includes the associated equation.  These image are derived from the source images that I used to make the video.  4k versions of these particular images are available to Patreons.

Higher Power Mandelbrot 

Higher Power Mandelbrot 

Higher Power Mandelbrot 

Higher Power Mandelbrot 

Higher Power Mandelbrot 

Higher Power Mandelbrot 

Higher Power Mandelbrot 

Higher Power Mandelbrot 

Higher Power Mandelbrot 

Higher Power Mandelbrot 

Higher Power Mandelbrot 

Higher Power Mandelbrot 

Higher Power Mandelbrot 

Higher Power Mandelbrot 

Higher Power Mandelbrot 

Higher Power Mandelbrot 

Higher Power Mandelbrot