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

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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Part I

Part II

Part III

Part IV

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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Iterations

Iterations

So, a complex number is an imaginary number together with a real number. It can be written as:

imaginary , real or (i , r) or
imaginary + real or (i + r).

Put simply, the Mandelbrot Set image is generated by iterating points from the complex plane (the set of all complex numbers), through the function z = z2 + c.

Each time a point is put into the equation, another point comes out. This ITERATION process produces a sequence of “points” that either escape to infinity (as happens with the points on the OUTSIDE of the Mandelbrot Set), or they get “trapped” in black region, in which case they are said to be INSIDE the Mandelbrot Set.