Mandelbrot Set

Fatou and Julia

Benoit Mandelbrot

M-Set How?

Complex Numbers

Imaginary Numbers

Iteration

M-Set Algorithm

Julia Sets

J-Set Algorithm

Part III

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Fractal

Copyright (c)

ButterflyEffect.ca

Lori Gardi

FractalWoman

lgardi22@hotmail.com

 

Part I

Part II

Part III

Part IV

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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Julia Sets

Julia Sets

The Julia Set(s) are a slightly different than the Mandelbrot Set as I will explain. For every POINT in the complex plane, there exists a set called the Julia Set each of which has a different shape and a different dynamic associated with it. In other words, every point in the complex plane generates a different Julia Set "curve" or image.

Also, it has been shown that the Julia Sets generated from the points on the INSIDE of the Mandelbrot Set form Connected Sets, and the Julia Sets that are generated from the points on the OUTSIDE of the M-Set form disconnected sets also known as Cantor dusts.

I won’t get the details of what this means at this point. The main point I wanted to make here is that there is a “fundamental” difference between the points on the INSIDE of the M-Set and the points on the OUTSIDE. Just remember:

Inside = Connected, Outside = Disconnected.