One of the biggest concerns when people learn math is that they think they will never use it or say they don’t use it every day. Even if they don’t think they’re using math every day, they might be seeing math without even noticing.

Fractals are geometric features like circles or squares but exhibit a special property: self-similarity, or the whole has the same shape as one or more of the parts. These geometric features are self-similar patterns on infinite scales, meaning that the same patterns continue to reemerge when we repeatedly “zoom in” on the pattern. Numerous examples in mathematics include the elaborate geometric features of the Sierpinski Triangle (seen below), the Koch Snowflake and the Mandelbrot Set, which can be created by a computer calculating a simple formula over and over.

But fractals are more than just a mathematical theory. There are many examples of fractals that appear in nature and elsewhere in our daily lives, including art. For instance, self-similar patterns frequently appear in the musical structure of songs. In nature, one of the most commonly discussed examples of fractals is romanesco, a vegetable closely related to broccoli and cauliflower. In fact, romanesco shares a repeating pattern where the number of spirals on a head of romanesco is tied closely with the Fibonacci sequence.

The Fibonacci sequence is a string of numbers (0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55,…) that continues forever following the rule that the next number in the sequence is created by adding the two previous numbers. For example, 0+1=1, 1+1=2, 1+2=3, and so on. This famous sequence of numbers appears elsewhere in geometry. When squares with the widths of these Fibonacci numbers are placed next to each other, it creates an aesthetically pleasing spiral giving rise to the Golden Ratio (approximately 1.61803398874989484820…). This ratio can be seen in examples of nature like romanesco or in architecture like the Parthenon.

We may not consciously use math every day, but math is all around us, and we see it a lot more than we think.

By David Fertitta

*Sources:
*http://mathworld.wolfram.com/Fractal.html

http://math.rice.edu/~lanius/frac/

https://plus.maths.org/content/os/issue55/features/kormann/index

http://fractalfoundation.org/about-us/our-mission/

http://fractalfoundation.org/resources/what-are-fractals/

http://fractalfoundation.org/fractivities/WhatIsaFractal-1pager.pdf

http://fractalfoundation.org/fractivities/FractalPacks-EducatorsGuide.pdf

http://mathworld.wolfram.com/Fractal.html

http://mathworld.wolfram.com/GoldenRatio.html