Any one who has, at one time or the other, played at dodging the wave at the beach will know that. A man made example of a chaotic system is the financial markets of the world. These, from the outside, appear to be random and unpredictable, but, as we know, each financial decision is a conscious decision and is far from random. Each step of the way computations are used, along with previous knowledge to make these decisions. Yet, due to the sheer complexity of dependencies, the results can often appear to be far from rational.
Different algorithms produce different amounts of complexity when iterated.
Also changes in a chaotic system can have different levels of impact. Each event has a constantly different amount of effect on the next step. The famous example is the butterfly effect, where it is claimed that the flapping of the wings of a butterfly can, given time, effect the direction of a hurricane on the other side of the planet. On the other side it may have no effect at all. It is this apparent lack of ease of prediction that creates what we call random effects.