When Healing Becomes Educating, Vol. 2 - Waldorf Research Institute

V-shaped peninsula that is another equilateral triangle with sides of length
1/3 (Fig. 2). If this step is repeated ad infinitum, the curve not only becomes
infinitely long but also changes direction at every point. It therefore reaches
infinitely more points than a line does, and it would be reasonable to say
that a Koch curve tries to be like a plane, without ever being a plane. The
dimension of the curve can be shown to be 1.2618. This is a fractal and at
the same time one hundred per cent self-similar. We can take any part of the
curve and any scale, the image will always be the same.
The term “fractal” was coined by Benoit Mandelbrot in 1975. He had
been considering irregular and seemingly random phenomena such as
fluctuations in the price of cotton, or recurrent noise problems in telephone
lines used to transmit information from computer to computer, which were
liable to cause major errors. Mandelbrot’s brilliant work showed that all
the basic patterns involved recurred on all kinds of different scales. There
would be hours in the day when errors came up in bunches, compared to
other hours that were problem free. Analysis of the problem hours showed
phases when errors were many and others that were problem free. When
smaller periods were chosen, the basic pattern of error peaks alternating
with problem free phases persisted. Mandelbrot showed that no period ever
had a consistent rate of error, which also meant that it was not possible
to calculate mean error rates. Yet the proportions of peak error and error
Fig. 2. Koch curve
Starting with an equilateral triangle, a new equilateral triangle is created on each side, with the process
repeated ad infinitum.
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