“Let it go, let it go, can’t hold it back anymore…” At this point I’m sure we all have heard the song “Let It Go” from Disney’s Frozen. I know I have it memorized. When I was listening to it for the umpteenth time, I realized there was a very interesting word buried in one of the lines. “My power flurries through the air into the ground; My soul is spiraling in frozen fractals all around…” What in the world is a fractal? Well, read on to find out!
According to dictionary.com, a fractal is “a geometrical or physical structure having an irregular or fragmented shape at all scales of measurement between a greatest and smallest scale such that certain mathematical or physical properties of the structure, as the perimeter of a curve or the flow rate in a porous medium, behave as if the dimensions of the structure (fractal dimensions) are greater than the spatial dimensions.”
In case you were as confused as I was after reading that definition, a more simple definition can be found at http://fractalfoundation.org/resources/what-are-fractals/. They say “a fractal is a never-ending pattern. Fractals are infinitely complex patterns that are self-similar across different scales. They are created by repeating a simple process over and over in an ongoing feedback loop.” These “never-ending patterns” were first discovered in 1975 by Benoît Mandelbrot. He discovered a set of numbers called the Mandelbrot Set. When the numbers belonging to this set were graphed, they created a pattern.
The Mandelbrot Set
Courtesy: “Mandel zoom 00 mandelbrot set”. Licensed under Creative Commons Attribution-Share Alike 3.0 via Wikimedia Commons
These beautiful, infinite patterns are called fractals. The word fractal was created by Mandelbrot and was derived from the Latin word “fractus” which meant “broken.”
Approximate fractals are found in nature. They’re called approximate since they don’t repeat infinitely like true fractals that are only found in math. Approximate fractals can be seen in heartbeats, pineapples, ferns, DNA, broccoli, lightning, and snowflakes.
In case you want to know more about fractals, here’s a short video about them.
If you want to know even more, here’s a video from Dr. Jason Lisle talking about these beautiful patterns. It’s a little long, but if you have the time, it’s definitely worth it.
Thanks for reading!