Transitivity

In some systems there are starting states which drift all over the place as time goes by.

If we follow such a starting state for long enough, it eventually passes through any little piece of the state space we care to consider.

See how the starting state shown eventually passes through the little patch shown in green.

It turns out that if there is just one of these "wandering" states, then they will be everywhere you look.

This gives the appearance of random wandering often associated with chaos.

This classic feature of chaotic systems is called "transitivity".