At first sight the Koch
curve (see Koch Snowflakes) appears to be part
of a mathematical fantasy world. Enlarge any part of the Koch curve and the
new image is identical to the original  it is selfsimilar. This property
of selfsimilarity is the key behind all fractals.


Original Sierpinsky gasket  
Fern  
Fractals are amazing objects
as they are easy to construct but their composition has an infinite structure.
To fully understand this, we compare a fractal to a smooth curve. Both are
made up of infinitely many points but as we magnify the smooth curve it flattens
out and eventually appears almost straight. The position of a point on the
smooth curve can be approximately determined by considering the points before
and after it. However no amount of magnification of the Koch curve will produce
a smooth region. Without prior knowledge of the Koch curve we cannot predict
the position of a point from points close by. One way to quantify this difference
is to use dimension. With this is mind, Monique Breslin and John Belward in the Department of Mathematics at The University of Queensland have been analysing Queensland's rainfall data. 

In the past 1dimensional smooth curves have been used to model the rainfall. But Monique and John argue that this assumes rainfall patterns on the 1st and 3rd days can be used to predict the rainfall on the 2nd day, which in general is false. Instead they have found that the infinite structure of fractals provides a much closer model for rainfall patterns. In some parts of northern Queensland the dimension of the curve is higher than 1.6 implying unpredictable rainfall patterns. Even in drier parts it is 1.3, and still unpredictable. With this research Monique and John are working with the Department of Primary Industry to improve weather information for Queensland agriculturalists. More on Fractals: 
