Probability theory is concerned with regularities in random processes, such as laws of large numbers and limit-shape theorems. Recent work by researchers at the interface between probability and combinatorics shows that many of these regularities apply, sometimes in dramatically heightened form, to quasirandom systems: simple deterministic systems whose microscopic behavior is designed to mimic the average case behavior or random systems. Quasirandom processes often possess a richness of structure not evident in the random processes that inspired them. This talk will address the questions: Where do pictures like the one at http://rotor-router.mpi-inf.mpg.de/1Bio/?rotorseq=2 come from? And what are they telling us?