Fractals and life (part I)

Well, these are a special breed of mathematical beasts, they are ever growing collections of dots and no matter how deep you zoom them in you'll get about the same picture as you got when looking at the original.
As an example, one of the most intuitive ones, we will consider Sierpinski's triangle: let us take a triangle with all sides equal and join the middles of its sides. We thus get four smaller triangles. Lets cut off the one in the center. We now have only three triangles in the corners, and repeat for each one of them the same procedure: join middles and cut the center triangle. If we infinitely repeat the procedure we would obtain something that looks like this:

Where does life use these kind of tools? Frosted window patterns, broccoli, shattered compact discs, Scandinavian fjords and the list goes on. 

References:

Artwork: http://www.zeuscat.com/andrew/chaos/sierpinski.html

Examples: http://en.wikipedia.org/wiki/Main_Page