In the 1960's the mathematician and meteorologist Edward Lorentz was attempting to simulate the behaviour of the atmosphere on a computer. At that time it was assumed that all that was needed to provide the perfect weather report was the right model and big enough computing grunt. Lorentz's model for atmospheric convection consisted of the following three ordinary differential equations:
Now, these might look
very simple equations, but due to the non-linear terms they cannot
be solved analytically. A plot of the numerical values calculated
from these equations using particular initial conditions is anything
but simple, as can be seen from the picture above. Starting from
any initial condition the calculations will approach the paths displayed
in the image, but the actual path followed by the calculations is
highly dependent on the initial conditions. The strange shape in
the picture attracts points outside of it and as such is called
an If we were to magnify one of the
lines in the shape we would see it was not just one line, but many.
Continual magnification yields the same result, hence the shape
is said to be What Lorentz had shown was that the future state of the system was very sensitive to the initial conditions used for the calculation and hence even a deterministic system could be inherently unpredictable in the long-term. With reference to Lorentz's strange attractor the famous statement on chaos says that the flapping of a butterfly's wings in Tokyo can cause a tornado in Texas. |