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Mother Nature’s Mathematical Patterns

Written by Mohini Shanker– Eco Hub Eco-Rep

We’ve all seen patterns in nature, but how–and why– do they actually form? How do they bring together concepts of math and beauty? Let’s jump into one pattern that finds itself in several different natural forms: tessellations.

Tessellations are geometric patterns consisting of shapes that cover a 2D or 3D surface with no gaps or overlaps.

A 2-dimensional tessellation made of red, green, and blue rhombuses at different orientations that look like cubes when put together.

While tessellations are generally thought of as highly mathematical or derived patterns, they actually have many natural occurrences! Here are some of the more commonly perceived natural tessellations:

Arrays are the most recognizable tessellations in nature, occurring in patterns like honeycombs. Honeycombs form a hexagonal pattern that overlaps itself neatly without gap or overlap. The ubiquity of honeycombs actually led to a subset of tessellations being named after them, with n-honeycombs being defined as a tessellation in any n number of directions.

A honeycomb with bees crawling across it.

Tiling is a pattern that we’ve seen more than we think: with scales!

Green fish scales in a tiled/overlapping pattern.

Tiled patterns can be found on reptiles, fruits, and flowers. For example, the snake’s head fritillary has a naturally tiled pattern on the outer petals:

A snake’s head fritillary, purple with a checkerboard pattern on the petals.

While patterns of scales generally include some overlap, the geometric shapes created by the overlap can be depicted as a tessellation.

There are other patterns, such as crystals and fractals, that resemble tessellations without being exact (with no gaps or overlap), or with distortions. The growth of Brussel sprouts, for example, can be seen as a 3-dimensional fractal spiral.

A stalk of Brussels sprouts, with sprouts growing in a helical pattern down the stalk.

Spirals are most commonly seen in flowers and shells, like the seed heads of sunflowers shown below.

A sunflower seed head with seeds in a natural spiral pattern.

While distorted and not an exact tessellation, the pattern forms naturally and has a similar mathematical basis.

Natural patterns are a perfect reminder of how science and nature affect how we perceive beauty. Next time you’re outside, keep an eye out for new patterns, big or small!


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