Self Similarity

While mathematicians possess many complicated computational methods to define a true fractal, they are really not that simple to comprehend (as opposed to many other complex mathematical ideas). A fractal is a complex shape which, when viewed in finer and finer detail, shows itself to be constructed of ever smaller parts, similar to the original.

The most common such familiar analogy that is used in explanations of fractals, is that of the measurement of a shoreline.

When one zoomed in on that pattern, an even finer version of the same pattern was displayed. This could be repeated infinitely, to finer and finer levels – a feature which is known as self-similarity.

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What is really interesting about all of this is the fact that fractile geometry breaks down into three basic shapes:

circle

square

triangle

In fact, both the circle and the square are composed of triangles...

So, what's the point of knowing all of this?

Ecologists have found fractal geometry to be an extremely useful tool for describing ecological systems. Many population, community, ecosystem, and landscape ecologists use fractal geometry as a tool to help define and explain the systems in the world around us. As with any scientific field, there has been some dissension in ecology about the appropriate level of study.

For example, some organism ecologists think that anything larger than a single organism obscures the reality with too much detail. On the other hand, some ecosystem ecologists believe that looking at anything less than an entire ecosystem will not give meaningful results. In reality, both perspectives are correct. Ecologists must take all levels of organization into account to get the most out of a study. Fractal geometry is a tool that bridges the "gap" between different fields of ecology and provides a common language.  Read more

The importance of fractal geometry is that it provides an answer, a comprehension, to nature, the world, and the universe. Fractals occur in swirls of scum on the surface of moving water, the jagged edges of mountains, ferns, tree trunks, and canyons. They can be used to model the growth of cities, detail medical procedures and parts of the human body, and for some be used to create art.  And, for me that's appealing.