Surely fractals and chaos are everywhere, from parts inside our body to satellite images of coasts and river deltas. Even in things which look random, like a dripping faucet, you can find a chaotic pattern; which means it's a non-linear/non-predictable pattern but it isn't random at all Surely fractal formulas are useful for recursive building, that is achieving complex structures with very little instructions. Our DNA surely contains these short powerful formulas or the instructions to build us would be too complicate to be coded in a small place There is a great book which inspired me on all those things, a book which can be read like an amazing story of discovers and normal (but genial) people behind them, it's 'Chaos: making a new science' by James Gleick
As you describe, indeed fractals are everywhere but in discrete existence. In that tree or flower, a river or coastline to which you allude. But what if they were all just elements of some super fractal. The mother of all fractals. As for chaos there can be no such thing in the sense the word implies. All that we observe is logical conclusion to all that has gone before. Its a path not a park in which we meander aimlessly. I shall look out for the book.