Is the order in the universe just the result of random patterns that form from time to time?
Absolutely not. It seems that the entire past history of our universe has been spent in a phase with incredibly well defined and regular natural laws. Any variation in the basic physical laws would show up in our not being able to match observations with predictions beyond some key epoch when the 'changeover' happened. Currently, Big Bang theory predictions are based on the assumed uniformity of the natural laws all the way back to something like one trillionth of a trillionth of a trillionth (10-36) of a second after the Big Bang. No one knows what really happened before then, although there have been a few discussions in the technical literature about 'Chaotic Gauge Theory'. This theory proposes that instead of a state of Perfect Symmetry, the universe emerged from a state of Perfect Chaos where there were no laws at all. It was a state of complete anarchy, and perhaps no time, space and cause-and-effect to boot. There are many examples in nature of systems undergoing phase changes (ice to water), and perhaps initially the universe WAS in some chaotic state. Our natural laws emerged from chaos.