What Makes Mandlebrot and Julia Sets Fascinating in Fractal Mathematics?

[Hyperreality]

I am sure the same goes for you lot, I am fascinated by the complex patterns of fractals and recently found out it is generated by extremely simple algorithms (which takes weeks to run).

What do I actually need run some algorithms that generates fractals?

 

[jim mcnamara]

You can download Winfract or ther fractal generators for Windows, as a start.

http://spanky.triumf.ca/www/fractint/getting.html

This runs on Windows 95 and newer versions of Windows, Fractint is a DOS program.

 

[HallsofIvy]

"Which takes weeks to run"? What vintage computer are you running these things on?

Many years ago, I wrote a program to draw Mandlebrot's set (and the Julia sets). I would start it running and go to class. When I got back about an hour later, it would be almost finished! Now exactly the same program take a few seconds.

Julia sets, J_c, are those starting points (thought of as complex numbers: (x,y)= x+ iy= z), z₀, for which the sequence z_n+1= z_n²+ c converges.
The Mandlebrot set, sort of an "index" to Julia sets, are those c values for which z_n+1= z_n²+ c, with z₀= 0, converges.