This Issue is covered in Stephen Wolfram's book A New Kind of Science.
In this book Stephen Wolfram analyses simple cell systems that have simple rules this topic is called Cellular Automata.
Through Stephen Wolframs analysis He finds that a simple rule called rule 30 cellular automata produces just as much complexity as when he try's to produce complexity with more complex systems.
He then analysis a bit although I personally feel not enough of the polynomial universe as to see if such complexity and unpredictability can be reproduced at a more optimal level than having to go through the step by step system of cellular automata rule 30.
It's a very heavy but Interesting book If you have been of the view that highly complex systems require more complex systems to produce then I thoroughly recommend that you read this book.