Math Patterns in Nature

Have you ever thought about how nature likes to arrange itself in patterns in order to act efficiently? Nothing in nature happens without a reason, all of these patterns have an important reason to exist and they also happen to be beautiful to watch. Check out examples of some of these patterns and you may be able to spot a few the next time you go for a walk. 


Animation of simple shapes splitting of into smaller shapes which displays the fractal pattern

A fractal is a detailed pattern that looks similar at any scale and repeats itself over time. A fractal's pattern gets more complex as you observe it at larger scales. This example of a fractal shows simple shapes multiplying over time, yet maintaining the same pattern. Examples of fractals in nature are snowflakes, trees branching, lightning, and ferns.


Animation of particle strands forming a spiral pattern

A spiral is a curved pattern that focuses on a center point and a series of circular shapes that revolve around it. Examples of spirals are pine cones, pineapples, hurricanes. The reason for why plants use a spiral form like the leaf picture above is because they are constantly trying to grow but stay secure. A spiral shape causes plants to condense themselves and not take up as much space, causing it to be stronger and more durable against the elements. 


Animation of a fractured surface displaying the voronoi

A Voronoi pattern provides clues to nature’s tendency to favor efficiency: the nearest neighbor, shortest path, and tightest fit. Each cell in a Voronoi pattern has a seed point. Everything inside a cell is closer to it than to any other seed. The lines between cells are always halfway between neighboring seeds. Other examples of Voronoi patterns are the skin of a giraffe, corn on the cob, honeycombs, foam bubbles, the cells in a leaf, and a head of garlic.