However by thinking mathematically you can generate the
pattern that corresponds to as many folds as you like. By two new lines at the
right angles to each other. The first pair of new lines is to the right, the
next pair to the left, and so on.
From a mathematically point of view, the pattern can be
developed to correspond to infinitely many folds. It is no longer a collection
of lines, but forms a filled-in-shape.
The word ‘fractal’ was coined by the French mathematician
Benoit Mandelbrot to describe a shape that is irregular at all scales. Many
fractal can be split into parts. A shape that has this property is said to be
self-similar.
Fractal are also used in many practical situation, from
modelling internet traffic and fluctuation in word stock markets, to medical
research. Our own body contains a myriad of self-similar fractal systems: for
instance, our circulatory systems have this structure.
Another surprising fact is that, despite the rough shape of
the heighway dragon. In fact this can be done in several different ways. You can
prove that the property was true for any number of odd numbers. You can look
for mathematics in all kinds of situations: asking yourself the tantalising
question ‘What would happen if…..’
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