The Golden Spiral: Complex Geometries in Nature


What do hurricanes, galaxies, sunflowers and the human ear have in common? They all have inherent spiral shapes that conform almost perfectly to the ‘golden spiral’, which is derived from a mathematic formula. A golden spiral is a logarithmic spiral with a growth factor of ‘Phi’, which is the golden ratio – that means it gets wider by a factor of Phi for every quarter turn it makes. Here are 20 photos of 11 examples of golden spirals in nature.




(images via: nickton, wikimedia commons 1 + 2)

Look closely at the center of a sunflower and you’ll see the golden spiral in a repeating pattern. This amazingly complex layout of seeds is a perfect example of the golden proportion in nature. For a sunflower, growing in this manner creates the most compact pattern possible with no gaps from beginning to end.



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Here is the Fibonacci spiral in the swirl of a galaxy, just as it appears in so many other natural forms.

Succulent Plants


(images via: art poskanser, duff_sf, randy robertson)

Even succulent plants like aloe display the golden spiral with amazing perfection. Plants grow new cells in spirals, which is how this pattern appears. It works to the plant’s advantage by preventing new leaves from blocking older leaves’ access to sunlight, directing the maximum amount of rain and dew to the roots.



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It may not be as evident as the other examples at first, but the spines on this cacti have grown in the same spiral pattern as the sunflowers and succulents.



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Look at the images of the galaxies compared to this satellite image of Hurricane Isabel. Isn’t it striking how similar they are? While galaxies and hurricanes may not seem to have much in common, they both exhibit the mathematical curve of a logarithmic spiral.



(images via: sudhamshu, wikimedia commons, bernadettemacphersonmorris)

Even certain species of spiders form their webs in spirals that closely approximate the golden spiral.

Sea Shells


(images via: jitze)

Sea shells are among the most striking examples of the golden spiral at work. When cut in half, a nautilus shell displays its chambers and its spiral structure becomes even more apparent.



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The golden spiral is highlighted in this image of a leaf from a bromeliad plant.

The Human Ear


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Even the human ear conforms to the shape of the golden spiral. This shape helps collect sound waves and direct them to the inner ear.



(images via: koshyk)

The repeating golden spiral can be found within the petals of a rose.

Pine Cones


(images via: daniel oines, wikimedia commons)

Yep – it’s in pine cones, too. Just as with sunflowers and succulent plants, the pattern of seeds on a sunflower can be found in repeating sunflowers in either clockwise or counter-clockwise motion.