Artificial Forms
Fractal Dimension
Fractal Geometry
More Examples
Why Fractals
The Lorenz Equations
Nonlinear Geoscience

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.