The golden ratio manifesting in nature

The universe may be chaotic and unpredictable, but it’s also a highly organized physical realm bound by the laws of mathematics. One of the most fundamental (and strikingly beautiful) ways these laws manifest is through the golden ratio.

It’s not hard to find examples of this logarithmic phenomenon in nature — whether it’s a simple houseplant (like the aloe plant above) or an expansive spiral galaxy (like the spiral galaxy, Messier 83, seen below), they all originate from the same mathematical concepts.

Messier 83, a spiral galaxy located 15 million light-years away from Earth. (Photo: William Blair/Hubble Heritage Team/NASA/ESA)

The golden ratio (often represented by the Greek letter ϕ) is directly tied to a numerical pattern known as the Fibonacci sequence, which is a list composed of numbers that are the sum of the previous two numbers in the sequence. Often referred to as the natural numbering system of the cosmos, the Fibonacci sequence starts out simply (0+1= 1, 1+1=2, 1+2=3, 2+3=5, 3+5=8…), but before long, you’ll find yourself adding up numbers in the thousands and millions (10946+17711=28657, 17711+28657=46368, 28657+46368=75025…) and it just keeps going on forever like that.

When a Fibonacci number is divided by the Fibonacci number that came before it, it approaches the golden ratio, which is an irrational number that starts out as 1.6180339887… and, once again, goes on forever.

When the golden ratio is applied as a growth factor (as seen below), you get a type of logarithmic spiral known as a golden spiral.

golden ratio spiral

Learn more about the Fibonacci sequence and natural spirals in this fascinating video series by mathematician Vi Hart:

As Hart explains, examples of approximate golden spirals can be found throughout nature, most prominently in seashells, ocean waves, spider webs and even chameleon tails! Continue below to see just a few of the ways these spirals manifest in nature.

Chameleon tails

(Photo: Ryan M. Bolton/Shutterstock)

Seashells

(Photo: Tramont_ana/Shutterstock)

Fern fiddleheads

The curled up fronds of a young fern are known as fiddleheads. (Photo: Zamada/Shutterstock)

Ocean waves

(Photo: irabel8/Shutterstock)

Flower buds

(Photo: Romantsova Olga/Shutterstock)

Snail shells

(Photo: vvoronov/Shutterstock)

Romanesco broccoli

(Photo: Sergey Skleznev/Shutterstock)

Whirlpools

(Photo: Elaine Davis/Shutterstock)

Comfrey flowers

(Photo: Mikhail Melnikov/Shutterstock)

Pine cones

(Photo: bzanchi/Shutterstock)

Sunflower seed head

(Photo: Portogas D Ace/Shutterstock)
CATIE LEARY

July 27, 2015, 9 a.m.

Full article:

Source: How the golden ratio manifests in nature | MNN – Mother Nature Network

Advertisements

Leave a Reply

Please log in using one of these methods to post your comment:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s