Fractals as patterns of complex systems

I only sort of get this. I looked up fractals and saw pictures, read definitions, got examples. It's a concept that seems a little vague to me. I understood the examples like ferns and trees, clouds and mountains. Each branch has a likeness of the whole tree when viewed from a distance. Each enlargement is similar looking to the views from further away. There were some cool pictures I saw that showed each enlargement, similar to the previous, and each time it was enlarged you could see that you could just keep going and going and going . . . I really liked that idea, that there was no end in either direction. Just the repeated pattern stretching out forever.