Inferno #04 22 июня 2003

Программирование

Mathematics - Mandelbrot fractal.

          Mandelbrot fractal.

(C) Alone Coder


  Here are some friends I got the question, what is a fractal, 
and why you need it. The second question to answer, I can not, 
but the first answer right here and as fully as possible! 
Although these familiar anyway Spectrum magazine do not read!



                   1.


   Fractal is the figure or pattern
preserving (-ies) a complicated structure when scaled to any 
number of times. These fractals can be successfully used in 
demomeykinge. 

   Here's a picture:



   This is a general view of the Mandelbrot fractal with
minimal increase. Mandelbrot fractal is a two-dimensional 
pattern, defined on the complex number plane. 

   Properties, which manifest themselves in this fractal 
scaling can be understood by the following picture: 



  (The picture shows a fragment of a fractal around the point 
(.35703211; .57944996) With an increase of 1 billion times.)


   Now you understand? Continue.

   Mandelbrot fractal (or "Mandelbrot") generate a single 
point. Each point represents the following calculation. 

   Let the coordinates of points equal to (cx; cy).

   We assume their components of a complex number C = cx + i * 
cy, where i = √ (-1). 

   Initialize a complex number Z = C.

   We assume Z = Z ¤ + C, while | Z |