Chapter 2: Fractals! And Geometry in Nature

              Geometry. We all took it at the beginning of high school, and most of us have just passed it off and had little thoughts about it since. But besides basic algebra, it is the math most relevant and useful to everyday life. Whether you are measuring the dimensions for a new workbench in the garage, or fencing in the back yard, we all use a little bit of geometry every day. Although the biggest and mostly unknown use of geometry is in the world of nature around us through the exquisite design of fractals.

                So what exactly are fractals? Well the very mathematical definition is that Fractals are infinitely complex and repeating patterns that are self-similar across different scales and are no-where mathematically differentiable.^(1.) More simply, fractals are repeating patterns found that expand out in the same pattern that can be described by mathematical formulas. They are found everywhere in nature and biology; from trees, mountains, and rivers, to chemicals and basic atomic structure, and even in our very own DNA is a fractal pattern. ^(2.) So you actually have trillions of fractal patterns inside of you right now, and all around yourself.

 

 Two Fractal patterns found in nature

          So why does any of this matter? And why should you care? Well besides the fact that they are beautiful and immensely interesting, it is integral to understanding them to be able to study anything about our natural world. The leaves of any tree grow in a fractalated pattern. The way electricity flows through an object or substance, is in a fractalated pattern. The way a mountain is formed when two tectonic plates collide, is in a fractalated pattern. Are you beginning to see the big picture? Mathematics and geometry didn’t come out of thin air, and are integral to the world around us from the most micro parts of our world, to the absolute largest.

The mandelbrot equation and its resulting fractal graph

              We also use them in our non-natural world as well. Fractal art is a booming industry as many people deeply appreciate the beauty found in the patterns. Fractal patterns are also used extensively in the animation industry, as they are used to render characters in scenery for movies and video games. Since our body is composed of so many naturally occurring fractals, researchers at Harvard and Johns Hopkins have started using them in the medical field to help diagnose diseases such as cancer and emphysema. ^(3.)  Beyond that, they are used in fields such as electronics, geology, and astrology. So as you can see, math is all around us, you just have to know where to look.

 How fractal examination is used to detect lung cancer

 Fractal Art

 Animation rendering using fractals

Sources:

1.) "Fractal." Wikipedia. Wikimedia Foundation, 06 Nov. 2014. Web. 11 June 2014. <http://en.wikipedia.org/wiki/Fractal>.

2.) "Patterns of Visual Math - Fractals in Nature." Patterns of Visual Math - Fractals in Nature. N.p., n.d. Web. 11 June 2014. <http://www.miqel.com/fractals_math_patterns/visual-math-natural-fractals.html>.

3.) Haggit, Craig. "How Fractals Work." HowStuffWorks. HowStuffWorks.com, 26 Apr. 2011. Web. 11 June 2014. <http://science.howstuffworks.com/math-concepts/fractals4.htm>.

If you would like to learn more, please check out the great site Fractal Foundation:

http://fractalfoundation.org/