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Dr. Christopher S. Baird

Why don't scientists use fractal concepts more considering that fractals are everywhere?

Category: Physics      Published: November 26, 2013

Although fractals are beautiful, they have limited fundamental physical significance. Public Domain Image, source: Christopher S. Baird.

First of all, fractals are not everywhere. Fractals are shapes that are self-similar in nontrivial ways at several different scales, such as the shape of a tree's branches or a coastline. The arrangements of atoms in typical bulk solids are not fractal; they are crystalline. The shapes of large astronomical bodies are roughly spherical and not fractal. The structures of polymers are chain-like, the shapes of laser light waves are sinusoidal, the orbits of asteroids are elliptical, and the patterns of honeycombs are hexagonal lattices. None of these shapes are fractal.

More importantly, scientists use fractal concepts infrequently because fractals are descriptive and not prescriptive. In other words, fractal concepts can convey the general shape of a tree, but can't tell you why the tree has this shape. For such information, you have to dig deeper into the underlying biology. Since science is mostly concerned with discovering the underlying physical principles at work, and not just describing the shapes of things, fractal concepts find limited use in scientific investigations. Fractal concepts can be useful as preliminary empirical models when the underlying mechanisms are unknown or are too complicated to model. But the end goal of all science is the discovery of the basic mechanisms and not just the development of empirical models.

To non-scientists, fractals may seem much more important than they really are. There are perhaps a few reasons for this.

First, fractals are beautiful. Their beauty makes them inherently attractive and engaging to humans. But beauty only bestows on an object artistic and personal value. Beauty does not make an object more scientifically significant or useful. It is the job of the artist to create objects of beauty. It is the job of the scientist to correctly predict physical outcomes. If the boring shape of an ellipse better describes the orbit of the moon than a beautiful fractal curve, the scientist goes with the boring ellipse.

Secondly, fractals seem more important to non-scientists because they are accessible. The mathematics of quantum theory is incomprehensible to all but those who have waded through several years of college-level quantum courses. The details of tree-branching biology is beyond the capacity and interest of most non-specialists. In contrast, the simple fractal principle of self-similarity is intuitive, understandable, and accessible. It is basic human nature for a person who is confronted with two explanations; one he does not understand and one he does; to accept the explanation that he understands as the one that is more correct and more significant.

Topics: chaos, fractal, geometry, shape