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\fs20 \pard {\cf2\fs28 An important example of deterministic chaos is 
the weather.  The forecasts are never for more than a few days into 
the future.  This is }{\cf2\fs28\b not}{\cf2\fs28  because our models 
of the weather are not complete. More powerful supercomputers and even 
more complicated models will not help much with the long term weather 
forecasts. }{\cf3\fs28 Edward Lorenz}{\cf2\fs28 , an MIT 
meteorologist,  showed this is the case in his influential paper }{\cf2
\fs28\i "Deterministic Nonperiodic Flow"}{\cf2\fs28  published in 1963 
in the Journal of Atmospheric Science. The weather is chaotic. Even 
with a perfect model of the weather it is not possible to predict it 
very far into the future. The reason is the so-called }{\cf2\fs28\i 
butterfly effect}{\cf2\fs28 , a name coined by }{\cf3\fs28 Lorenz}{\cf2
\fs28 . Let us assume that we have a good model of the weather. To use 
it to predict the future weather conditions we have to know the }{\cf2
\fs28\i initial conditions, i.e. }{\cf2\fs28 the weather conditions 
today.  }{\cf3\fs28 Lorenz}{\cf2\fs28  showed that for a particular 
model of atmospheric convection two }{\cf2\fs28\b initial conditions 
different by very little lead to two very different long-term predictions}{
\cf2\fs28 .  In this file we use the Euler approximation to integrate 
the three differental equations that Lorenz used to model atmospheric 
convection.  The strange attractor shown in the last graph is a 
fractal called Lorenz butterfly. }}
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\fcharset0\fnil Arial;}}\plain\cf1\fs20 \pard Initial conditions}
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