“Mathematics is the science of patterns, and nature exploits just about every pattern there is.”

– Ian Stewart, British mathematician

Philosophers and mathematicians have, for long, dedicated themselves to the cause of explaining nature, beginning from the very early ventures of ancient Greeks. After all, mathematics is, in its very essence, a search for patterns of all kinds – and what better place to find such irregularities than nature itself? A closer look into nature leads to some very interesting implications about the underlying beauty of our universe.

The Importance of Patterns

The struggle to find patterns in nature is not just a pointless indulgence; it helps us in constructing mathematical models and making predictions based on those models.

Consider the example of a crystal. A ‘perfect’ crystal is one that is fully symmetrical, without any structural defects. Of course, perfect crystals do not really exist; the physical world is rarely perfect. Mathematics is an abstract language, and the laws of physics serve to apply these abstractions to the real world. Assuming the object as perfect helps our cause. So, it is just that identifying a crystal as a symmetrical, uniform structure helps us in making approximations about its aspects.  Similarly, meanders or bends in rivers find explanation in the branch of fluid dynamics pertaining to physics. On a more cosmic scale, the characteristic spiral of galaxies that we are all too familiar with is a result of the laws of gravitation and can be modeled as such. Finding such patterns and abstractions facilitates our understanding of the world around us.

As it happens, several living organisms exhibit mathematical patterns too. One such sequence in nature, that is both common and fascinating, is the Fibonacci sequence.

The Famous Fibonacci

Often called ‘Nature’s Universal Rule’, the Fibonacci sequence is perhaps one of the most famous mathematical sequences. The origin of this sequence is much contested, although it is commonly attributed to the Italian mathematician Leonardo Fibonacci. In his famous work ‘Liber Abaci’, he introduced a hypothetical problem involving rabbits and employed the sequence to find the number of rabbits after a certain period of time.

In this sequence, each number is the sum of the two numbers that precede it. Take a look:


Something strange happens when the sequence approaches infinity. The ratio between two consecutive numbers converges to 1.61803… : ‘phi’, or as you might call it, the ‘golden ratio’.

Fibonacci Sequence in Nature

The Fibonacci sequence can be observed in a stunning variety of phenomena in nature.

Nautilus shells, one of the most iconic examples of the Fibonacci sequence, follow the proportional increase of 1.61.

The total number of petals of a flower is often a number present in the Fibonacci sequence, as with irises and lilies. Most pineapples have either five, eight, thirteen or twenty-one spirals; these are also Fibonacci numbers.

An iris has three large petals on the outside and three inner petals. Image courtesy: Pixabay.com

Similarly, consider the arrangement of seeds in the center of a sunflower. If you count the spirals present, once again, it is a number present in the Fibonacci sequence. If you categorize these spirals into those pointed left and right, you will get two consecutive Fibonacci numbers.

How strange is that?

One thing to keep in mind, though, is that the Fibonacci numbers are not observed everywhere. You can find just as many plants and animals that do not show Fibonacci numbers. The presence of a series of numbers in an object, does not necessarily mean that the figures and object are linked. As Robert Lamp says, ‘Sometimes a coincidence is just a coincidence.’ However, the Fibonacci numbers are so common in nature that they do reflect a certain connection.

An Evolutionary Perspective

Nature is not an entity that consciously follows mathematics (flowers are not the smartest.) Instead, it is mathematics that follows nature.

The golden ratio models nature’s way of packing things in the most effective and energy-efficient way. In the case of the sunflower head, and many other species, their arrangement represents the ideal packing of the seeds; there is no crowding in the center and no scarcity on the edges of the head. Similarly, by having a certain number of petals at a certain angle to each other, the flower ensures that each leaf receives an abundant amount of sunlight. It reflects the conclusion of evolution over millions of years, that for a particular species, this is the optimal arrangement of things. The Fibonacci sequence is just one simple example of the resilient and persevering quality of nature.

As we continue to scourge for mathematical patterns in our natural world, our understanding of our universe expands, and the beauty of nature becomes clearer to our human eyes.


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