**Fractal Geometry**

The word fractal was coined by French mathematician Benoit Madelbrot, who
developed what is known today as **fractal geometry**, a branch of pure
mathematics that has become a powerful tool for modeling and analysis in
many areas of the physical sciences and, not surprisingly, in the
geosciences, where for long a better descriptor of the intricate geometry
of nature that the traditional geometry of Euclides has been needed.

Fractals can describe convoluted, complicated natural forms much better
than the circles, spheres, triangles and squares and other regular forms
which are the only shapes Euclidean geometry can handle. A much quoted
phrase by Mandelbrot expresses this idea quite well:

*Clouds are not spheres, mountains are not cones, coastlines are not
circles, and bark is not smooth, nor does lightening travel in a
straight.*

Word of caution: Mathematical fractals have
geometrical and mathematical properties, they do not provide much
information about the physics of the object, its origin or its physical
properties. In addition, strictly mathematical fractals are not found in
nature; they are just convenient models of some natural objects. Fractals
become better models of natural objects when some randomness is included
in thier construction, for instance by slightly changing the rule at
randomly selected iterations. Another important point, already mentioned
above, but impossible to overemphasize, is that natural objects are
self-similar only over a limited range of scales, and thus fractals can be
used as models of nature only within a certain range of scales.