Can complexity emerge from lower levels of simplicity?

‘Is there really a Universe that is not designed from the top downwards but from the bottom upwards? Can complexity emerge from lower levels of simplicity?’ It has always struck me as being bizarre that the idea of God as a creator was considered sufficient explanation for the complexity we see around us, because it simply doesn’t explain where he came from. If we imagine a designer, that implies a design and that therefore each thing he designs or causes to be designed is a level simpler than him or her, then you have to ask ‘What is the level above the designer?’ There is one peculiar model of the Universe that has turtles all the way down, but here we have gods all the way up. It really isn’t a very good answer, but a bottom-up solution, on the other hand, which rests on the incredibly powerful tautology of anything that happens, happens, clearly gives you a very simple and powerful answer that needs no other explanation whatsoever.

Douglas AdamsSpeech at Digital Biota 2