If you throw a handful of sand, there will be almost no pattern to it, but if you look closely there WI be some points with more sand and some with less. You could find interesting looking things in this. When you look at the whole thing though it obviously doesn't have a pattern to it, except what our brain may find because it tries to find patterns, even when there aren't any.

I wouldn't call something that's just noise complex. I guess it sort of is by definition, but not in a way that's interesting. Normally when I think of "complex" it's something that has a purpose to it, but we can't identify easily, not something that's easy to identify but has no purpose. It's just a random distribution of matter with the rules of physics applied. It doesn't create anything that seems to have any purpose.