Mathematical Patterns In Nature

At a glance, nature may seem to be very random, with leaves, flowers sprouting from just about anywhere on the trees. But on close observation, one can find patterns emerging right from the subatomic level to the level of massive galaxies.

Nature is a beautiful creation. It’s a feast to the eyes. Beauty in its essence emerges from the patterns that are widely embedded everywhere in nature. Nature arranges itself in mesmerizing ways.

A very common example is the number of petals in flowers. Most flowers have 5 petals. If not 5, they can be 8, 13 or 21. These numbers are not random, they actually make a pattern, the Fibonacci Sequence. This pattern is the most visible in nature. Mathematics seeks to discover and reason all kinds of abstract patterns visible in nature.

Natural patterns can include symmetries, fractals, spirals, tessellations and waves to name a few.

Symmetry is extensively prevalent in nature. Many flowers, leaves, and animals like starfish and sea anemones have radial symmetry. Animals that move in particular directions generally have mirror or bilateral symmetry. Another very beautiful natural creation, the snowflake, surprises us with extremely complex yet very closely symmetric and unique patterns. Snowflakes generally have six-fold symmetry.

Butterflies and moths have exquisite, detailed patterns on their wings. Their wings are accurately identical.

Spirals are very common in seed arrangements in flowers, leaves on stems, and animals like molluscs (their shells). Plant spirals can be seen in sunflowers, phyllotaxis. Some plants like pine cones can even have multiple spirals going both clockwise and anticlockwise. These can be mathematically generated using Fibonacci numbers (where the subsequent number is the sum of the last two numbers). A very common example is the number of flower petals. Many flowers have just 3 petals. If not 3, they favor numbers like 5,8,13, and 21. These numbers are actually in the Fibonacci sequence. We can easily find Fibonacci numbers in the spiral formed by individual flowers in their seed arrangements like sunflowers, daisies, cauliflowers and broccoli.

Meanders are snaky curves often formed by fluids going around obstacles. Common observations can be made in rivers, where the water meanders past rocks. Also clouds during windstorms take such curvy ways. As soon as the path curves slightly, It further keeps on increasing the curvature and forms helical patterns.

Tessellations are patterns made by repeatedly tiling the same or similar shapes. Examples of tessellations are honeycombs (several hexagonal compartments arranged in striking symmetry), wasp nests and animal skins like that of snakes, pangolin. Many minerals found naturally deep down the surface of the earth show intricate crystal patterns of repeated geometry.

Waves and Sand dunes

Waves are oscillations that move through water, making visible chaos. Similarly, when winds pass over vast sands in deserts, they create dunes. Dunes are repeating curves of many types like crescents, parabolas, domes, sword shapes.

Wind waves are sea surface waves that create the characteristic chaotic pattern of any large body of water, though their statistical behavior can be predicted with wind wave models.

Everything in nature exists for a reason. These patterns and regularities not only impart beauty to nature, but also are stunning examples of smart and efficient designing. Nature’s architects are not us humans, but seemingly small animals, plants, and other organisms. The beautiful symmetries in flowers like lotus, daisies, and the enveloped petals of roses are all very organized and regular.

Many people like to collect seashells. They are indeed beautiful. Most of them are adorned with growth spirals.

Other animals that display art on their bodies are snakes, pangolins, fishes. These animals have scales on them that are organized in regular patterns which are beneficial to these creatures, like camouflaging in order to hide from enemies or catch prey.

Nature never fails to surprise us. Every creation leads us into a beautiful discovery, new or even repeating patterns. All these patterns hold great importance in literature or art, but as you have now seen, they can be very well explained by theories of mathematics and science. Mathematics is indeed a beautiful language. It subtly explains the mysteries of nature and the patterns emerging everywhere.

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