An image of totally 4 pixels (2px*2px) has a total of 16 different
combinations in a colordepth of 2 colors (black/white). The
mathematical formula of this statement should be:

(x*y)^c

where "x" is horizontal image size in pixels
where "y" is vertical image size in pixels
where "c" is colordepth

(2*2)^2 = 16

Imagine an archive of all image combinations in 32*32 pixels of black and white. 

(32*32)^2 = 1 048 576

I want to process this task on my desktop by software like Macromedia
Director or something similar, but having troubles finding a correct
algorithm for this. Could you please help me?

Thanks,
Albert

I think the math is backwards in your estimate of the number of images
you could have. Each image will have 32*32=1024 pixels, each of which
can have 2 colors (black or white). So there are 2^(32*32) possible
images, which is about 1.8*10^308 images, more than you could ever
store on your web server.

If you want to pick among these images at random, your best bet would
be to write a script on your web server that will generate a random
1024-bit number (or 32 random 32-bit integers). Then you could use a
gif library or some custom code to return a .gif or .bmp file which
uses all the random bits as the pixels of an image.