You may know the golden ratio is found in seashells and flowers, but the sacred geometry of the golden spiral, and the Fibonacci sequence also comes up in animals. Here’s just 10 examples of the golden ratio in animals to help you see it next time you’re out in nature!
1. Starfish
As I discussed in depth in my article about the number five, any time we see a regular pentagon, we have the essence of golden ratio and fractal geometry. A regular pentagon has all the sides the same. The starfishes arms try to form so that they are all equal in length. For example, the ratio of the starfish’s “arm-span” compared to its arm length is the golden ratio.
2. Snails
The snail’s shell is a beautiful golden spiral. When the snail makes its shell, the proteins assemble in a spiral, starting from the center.
The rings of the spiral get wider as you go out, which is essential for golden spirals. Read on to see the difference between a Archimedes spiral and a golden spiral.
3. Bird Tracks
The birds toes form the three upper points of a pentagon and the lower edge forms the other two. The shape of the bird track have five-fold symmetry. Different kinds of symmetry, like pentagonal symmetry, is described in my article about rotational symmetry.
4. Chameleon Tail
The chameleon’s tail curls to wrap around branches and otherwise grab things. The shape of the tail goes from wider to more narrow at the end. When the chameleon’s tail curls, the growth factor of the spiral is the golden ratio, meaning the tail forms a golden spiral.
Golden Ratio in Animals: Golden Spiral vs. Archimedes Spiral
Quick break before we see the rest of the golden ratio in animals examples. Not all spirals are golden spirals. There are many different kinds of spirals. When the rings are the same width and don’t get wider like we see in the chameleon’s tail or snail shell, it might be an Archimedes spiral.
So not every spiral in nature is a golden spiral! If it gets wider, it probably is, but specifically, the growth factor of the spiral needs to be equal to the golden ratio.
5. Elephant’s head
The elephant’s head right away looks symmetrical and orderly. The ears, trunk, and width of the head are such that a regular pentagon is traced out. With five-fold symmetry, we have many different parts and proportions having the golden ratio when compared. For examples, look at the segments of the star in my post about why the golden ratio is important. (Section titled “What is φ?”)
6. Rabbit Populations
In the same post referenced above about the importance of the golden ratio, you can read about how the Fibonacci sequence, which arose from studying rabbit populations, is related to the golden ratio. The Fibonacci sequence describes how we expect rabbit populations to grow over time.
When each pair of rabbit has a pair of offspring every month, and each pair of offspring must mature for a month before reproducing, the population numbers follow the Fibonacci sequence. The Fibonacci sequence becomes an excellent approximation of the golden ratio after many generations, when the population is divided the by population a month prior.
7. Mammal Tracks
Like the bird tracks, the mammal tracks, like wolves, cats, and bears, have pentagonal symmetry. The mammal tracks have even closer proportions to a pentagon than any other animal tracks. Instead of three toes, the mammal’s four toes form the top two sides of the pentagon.
8. Octopus Tentacles
The octopus tentacles have two examples of the golden ratio. First, like the chameleon’s tail, it can curl up into a golden spiral. Then, the suckers follow the golden angle around the tentacle so they appear to line up as the tentacle twists.
9. Worker Bee Populations
The queen bee reproduces without any help from the male bees. As she creates new worker bees their umbers increase like the rabbits.
10. Bats’ body and face
The bat’s body, like our human body, has five-fold symmetry. This same five-fold symmetry is also repeated in the face shape.
Examples of Golden Ratio in Animals are Everywhere
There are many more examples of the golden ratio in animals than what is listed here. If you think of another one, comment it below!
