Not only can chaos be exhibited in fully deterministic systems, it can be exhibited in absurdly simple systems. The logistic map is an incredibly simple iterate

Not only can chaos be exhibited in fully deterministic systems, it can be exhibited in absurdly simple systems. The logistic map is an incredibly simple iterated function that exhibits highly chaotic behavior. It remains one of most mysterious things in mathematics, as far as I can tell. Studying it has consumed a lot of very smart people's careers.