The Beauty of Numbers in Nature

Posted by Michelle Chandra on

Much of my past artistic inspiration has derived from patterns in nature, whether that is the 24 hour cycle of our day, the arc of a double rainbow, or the circular spin of stars in the sky when captured via timelapse photography.

I recently decided to start a 100 day project in which I will work on creating as many generative art prints inspired by natural patterns over 100 days. As inspiration for my 100 Day Project, I decided to research the math behind patterns in nature starting with a book by MIT professor Ian Stewart - The Beauty of Numbers in Nature.

Patterns of the Natural World

The Beauty of Numbers in Nature dives deep into all of the many different patterns in nature such as:

  • spots and stripes of animals
  • hexagon tiling of beehive honeycombs
  • refracted light that makes up rainbows
  • spiral shape of Nautilus sea shells
  • fractal pattern of mountains, rocks, and plants
  • cyclical patterns like heartbeat, 24 hour day, ocean waves, sound
  • patterns related to the passing of time like the gait of animals
  • spherical shapes of planets, and their circular orbit around the sun

We can understand how these patterns emerge through mathematical rules (which are idealizations of the patterns we see in the world!)

What is a Pattern?

Patterns can be thought of as demonstrating order rather than randomness (although in nature, they are not found to be perfect mathematical order).

When formulating the Laws of Nature, Einstein determined symmetry is the foundation, symmetry is an important element of patterns. There is the bilateral symmetry of humans and animals, or the rotational symmetry of most flowers and sea creatures and physical patterns like rainbows.

 The circular sphere is a common pattern in our Solar System and the most symmetric object in our universe. The circular rotation of planets is responsible for Saturn's rings and Jupiter's striped atmosphere, along with Earth's 24 hour day and weather patterns.

Besides bilateral and rotational symmetry, tiling patterns are common such as the underlying lattice structure of crystals. The carbon lattice of graphite is made from parallel honeycombs resulting in a soft material, while diamond, which is also made from carbon is quite hard due to its tightly packed cubic lattice structure. 

Most patterns in nature emerge from self-similarity - small rocks when viewed up close look like big rocks (i.e. mountains) and demonstrate fractal patterns at work. Other examples of fractal patterns include plants, bushes, trees, coastlines, rivers, and clouds (most everything!) 

There are also patterns that can be found in "dynamic systems," which means patterns you find only with the passing of time such as the gait of animals, and the movement of insects and snakes. 

Stewart writes that "ours is a mass produced universe made from myriad copies of identical components."

How are Patterns Formed?

There is much about the formation of patterns that we don't fully understand. This includes how animal stripes and spots form, and predicting the weather beyond a few days. Alan Turing's reaction-diffusion chemical processes produce patterns like stripes and spots, so a similar process is thought to lead to patterns found in animal fur. There are many chaotic dynamics at work in our atmosphere which makes it difficult to predict the weather weeks in advance.

Some patterns are a reflection of an animal's growth such as the ever spiraling shell of the Nautilus, or the circular pattern of plants which starts with the circular shoot. Much of the symmetry underpinning plants has been found encoded on a genetic level.

Overall plant growth is spiral and related to the golden angle (137.5 degrees), which can be closely approximated by fractions formed from Fibonacci numbers. Plants often have petals that are Fibonacci numbers.

Cauliflower, and the seed heads of daisies and sunflowers are arranged in spiral swirls while Broccoli Romanesco forms as spirals within a spiral. To see why the golden ratio is so golden in relationship to flowers, check out this YouTube video:

There are also natural patterns that form as a result of both order and chaos. Snowflakes have ordered sixfold symmetry, but their formation in the atmosphere is a result of the chaotic dynamics of clouds. When water freezes, it turns into ice crystals, and the structure of those crystals is determined by the temperature in the atmosphere, and the supersaturation of the water molecules in the clouds.

Last Thoughts

The Beauty of Numbers in Nature is a very detailed, deep read on the myriad natural patterns of our universe, and how mathematicians have studied and duplicated those patterns. There isn't actually a lot of math in the book though! I found this book united many things I learned in graduate school but provided some much needed context. If you are looking to be inspired and see the natural world differently, then pick up this book!

About Dirt Alley Design

michelle chandra of dirt alley designDirt Alley Design was founded just off a dirt alley in San Francisco in December of 2016 by artist Michelle Chandra. Inspired by the beauty of street grids, Michelle invented maze maps in which she transforms street grids into mazes. 

My maze art isn't just decorative art for your home, it's a real puzzle maze you can solve (if you dare!) I think my maze maps are pretty cool, but don't take just my word for it! My maze maps have been featured in the Chicago Tribune, Forbes, Print Mag and Vice, to name a few!

100 day project 2019

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