I haven't put any thought to it whatsoever. So my answer is going to be as shallow as probably any answer can get. In nature, things don't get created in one straight simple process. The processes get repeated. Take the Sun for example. It wasn't created right after the Big Bang. The primitive stars were full of Hydrogen and didn't have enough materials to form complex things such as life. They died and new elements were created at their core and new stars were born out of their death. This process got repeated again and again. And it wasn't just one single process. The creation process was a sum of many different processes which themselves were composed of other processes and so on. When things get repeated again and again and again and again in time, and if it leaves a pattern in space, I guess you get fractals.

"As above, so below. As within, so without." ...I think that's how it goes.

The way I think of it, if the universe is perpetually expanding, wouldn't it make sense that everything within it must also expand? The whole bang thing is a fractal!

...I'm feeling a little dizzy now.

As natural selection tries to make living things more efficient, once it finds a perfect solution, it won't want to deviate from it. It's like finding the perfect chocolate chip cookie recipe- after so much trial and error, why would you choose anything but the most optimal recipe? And, if that one solution works for multiple things, hey, that works.

I'm actually very interested by Makarand's answer. I've never really thought of fractals that way before. I wonder if once the solution that's "just right" is found, it's used as a baseline- like how after learning basic drawing skills, artists will deviate from it, but always have that similarity. Each deviation would then have to find ITS own perfect solution, and then deviate, so it forms a repeating pattern. Huh.

This is another interesting subject that provokes us to think about infinity. I enjoyed all the comments posted previous to this. I think they all add some good insight to this subject relatively new to me. Makarand speaks about how the big band is sort of a fractal. With the aid of technology we are now able to study the 'infinite' space of the universe and atoms. So far, through our limitations we have perceived nature in duality night and day, male and female, me and you. Maybe these type of structures will entice our consciousness to think differently. How we are all part of something bigger.

I think that Fractals appear often in nature because when things grow, they grow by duplicating cells. We know that people start off as one cell, but then continuously duplicate until they become multiple-celled beings. This duplication process is something that happens in all different organisms in nature. This is why it makes sense for many things, when magnified, show smaller versions of the larger organism.