Small differences in initial conditions (such as those due to rounding errors in numerical computation) yield widely diverging outcomes for such dynamical systems, rendering long-term prediction impossible in general.
Chaos: When the present determines the future, but the approximate present does not approximately determine the future.
From 30-Second Theories:
You leave the house five minutes late - and miss your train to the airport. Then when you reach the airport, you have missed your flight and discover the next flight is not until tomorrow. A five-minute overrun has ballooned into a whole day's delay. This is an everyday example of what mathematicians call a non-linear phenomenon, where small effects do not necessarily have small consequences. Chaos Theory focuses on such situations, the outcomes of which are often neither totally random, not totally predictable.
'Nuff said.
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