To Atheists: how do you explain the existence of intelligent systems and organisms?

Sorry if this question is a little simplistic. I'm not trying to hatch the old 'watch-maker/watch' debate- I realize atheists reject the notion of a designer of the universe.

What I'd like to know is, is there an agreement among atheists or shared explanation for why intelligent organisms and systems can then exist? I find things like emergence are good at describing the process, and are therefore good at answering the 'how', but it doesn't (to my knowledge) give an explanation or reason behind the mechanism- why or how is it logically possible. How can unthinking, unintending particles coordinate and move in ways complex enough to make you think they have a mind of their own? What's the logical explanation?