Chaotic dynamics
chaotically. This has been discovered more than a hundred years ago by Poincaré und was re-discovered by Lorenz, among others, in the 1960th. A famous example is the Lorenz attractor (figure) which provides a simplified description of atmospheric motion.
Though the structure of motion, the butterfly
, is preserved, a dramatic change in the transitions between both wings may be caused by a minimal change of the initial position. Such a system is predictable only for short times - as is the weather.