The Fibonacci Sequence and Golden Ratio in Nature!

You have probably heard of Fibonacci's famous sequence: 1, 1, 2, 3, 5, 8..., and so on, with each term equalling the sum of the previous two terms. If you divide each term by the previous result, you will find that as the numbers get bigger, the ratio converges to 1.6182. 1.6182:1 is known as the 'golden ratio'. This seemingly random sequence has baffled mathematicians and scientists alike, as the sequence and its converging ratio keep appearing in nature. Here are just a few places they appear in nature:

Flowers

The Fibonacci sequence can be seen in two different places in flowers. The most visible place is the petals of a flower. Several flowers have petals that are numbers of the fibonacci sequence. Lilies have 3 petals, buttercups have 5 petals, and daisies have 34 petals, for example. Scientists have theorized that petals that fit the Fibonacci sequence absorb more sunlight, among other uses.

Additionally, the seeds a flower produces follow the Fibonacci sequence. The seeds bunch up in the middle and spiral out in the same shape as a Fibonacci spiral. 

Shells

The spiral shaped Nautilus shell perhaps most closely resembles the Fibonacci spiral. Scientists speculate that the reason shells tend to be shaped like the Fibonacci spiral is due to the natural order taking the most efficient route as possible to create a spiral. Below is a comparison between the spiral and shell.

Galaxies

Galaxies maintain the shape of a Fibonacci spiral, seemingly against Newtonian principles! Because the stars have differing angular velocities depending on their distance from the center of the galaxy, the spirals shouldn't remain intact. However, the stars on the outside move faster than expected, allowing the galaxies to maintain the spiral shapes!

And finally...

Cats!