Mathematics of Nature: 15 Visual Patterns

Mathematics seeks to discover and explain abstract patterns or regularities of all kinds.

Since the ancient Greek civilization, different philosophers and scientists observed reality to find structures that can be measured and predicted.For instance the astronomer Eratosthenes could estimate the diameter of the Earth with great accuracy in 228 B.C. using basic trigonometry. Others like Galileu, Newton, Fibonacci and Einstein among many others could create formulas to understand visible and unvisible world, allowing to explain patterns in nature at different levels.

Visual patterns are all around us and those regularities can often be explained and predicted by mathematics, physics and chemistry theories.

The spots and stripes of animals were studied by Alan Turing and other scientists after him, describing a mechanism that spontaneously creates spotted or striped patterns. The accuracy of Turing's theories could be proved by experiments like the angelfish's stripes that do migrate across its body over time.

Other patterns in nature have been studied and have a close relationship with mathematics like symmetries, fractals, spirals, meanders, waves and cracks but the truth is that visual patterns are often chaotic, and don't exactly repeat.

Below you can visualize some examples of patterns in nature.

How is it possible that mathematics, a product of human thought that is independent of experience, fits so excellently the objects of reality?

— Albert Einstein

A ripple effect is a situation in which, like ripples expand across the water when an object is dropped into it, an effect from an initial state can be followed outwards incrementally.


Sixfold symmetry in a snowflake


Spiral patterns are found in the phyllotaxis of Aloe polyphylla.


Cloud vortices in the cloud layer off Heard Island, south Indian Ocean. Chaos theory predicts such patterns.


Emperor angelfish (Pomacanthus imperator) with a striped pattern like the one studied by Alan Turing.


Honeycombs are composed of hexagons, six-sided polygons.


This pineapple shows 8 left handed helices and 13 right handed helices. Both are Fibonacci numbers. Their quotient is the golden ratio.


The Romanesco broccoli is one of the many examples of fractal in nature.


This image is of NGC 1300 is considered a prototypical example of barred spiral galaxies.


This group of ammonites found in Brazil is another example of spirals in nature.


Wind ripples photographed in Sistan, Southwest Afghanistan.


Earth in the Rann of Kutch cracking as it dries. The pattern of cracks indicates whether the material is elastic or not.


Plateau's laws describe the structure of soap films. Many patterns in nature are based on foams obeying these laws.


Fromia monilis (Seastar). Another example of symmetry in nature.


A crystal is scientifically defined by its microscopic atomic arrangement, not its macroscopic shape—but the characteristic macroscopic shape is often present and easy to see.

mathematics captures patterns that the universe finds pleasant, if you like—patterns that are implicit in the way the universe works

— Keith Devlin, mathematician

A movie inspired on numbers, geometry and nature, by Cristóbal Vila

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