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One of the fathers of
chaos theory is Edward Lorenz. The figure shows the evolution of ensembles
of initial points on the famous Lorenz “butterfly” attractor.
The two wings of the Lorenz attractor can be imagined as two different weather
types, say mild and wet on the left and cold and dry on the right. The initial
points represent estimates of the current state of the atmosphere; the arrows
show how subsequent forecasts are affected by the small initial errors.
The three panels show how the effect of these errors can vary depending
on the initial “true state”. When we are in a predictable state
(top panel), small errors in the starting conditions will not affect the
forecast: we can be confident that the weather will become cold and dry.
If, however, we are in a less predictable situation (bottom left panel),
the points stay together only for a limited time before diverging. While
we can be confident of the forecast for a few days ahead, we cannot be sure
if it will ultimately stay wet or become drier. Sometimes the situation
is so unpredictable that we can have little confidence in the outcome even
a short period ahead (bottom right panel).
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