How to program a fractal?

Question

I do not have any experience with programming fractals. Of course I\'ve seen the famous Mandelbrot images and such.

Can you provide me with simple algorithms for fra

Answer 1

The mandelbrot set is generated by repeatedly evaluating a function until it overflows (some defined limit), then checking how long it took you to overflow.

Pseudocode:

MAX_COUNT = 64 // if we haven't escaped to infinity after 64 iterations, 
               // then we're inside the mandelbrot set!!!

foreach (x-pixel)
  foreach (y-pixel)
    calculate x,y as mathematical coordinates from your pixel coordinates
    value = (x, y)
    count = 0
    while value.absolutevalue < 1 billion and count < MAX_COUNT
        value = value * value + (x, y)
        count = count + 1

    // the following should really be one statement, but I split it for clarity
    if count == MAX_COUNT 
        pixel_at (x-pixel, y-pixel) = BLACK
    else 
        pixel_at (x-pixel, y-pixel) = colors[count] // some color map. 

Notes:

value is a complex number. a complex number (a+bi) is squared to give (aa-b*b+2*abi). You'll have to use a complex type, or include that calculation in your loop.