The Hidden Design

“Nature uses only the longest threads to weave her patterns,” Physicist Richard Feynman wrote in 1965 in The Character of Physical Law “so each small piece of her fabric reveals the organization of the entire tapestry.” 

Around 342 years earlier, astronomer and physicist Galileo wrote in The Assayer (II Saggiatore) “the universe – which stands continually open to our gaze, cannot be understood unless one first learns to comprehend the language and interpret the characters it is written in. It is written in the language of mathematics, and its characters are triangles, circles and other geometrical figures.” 

Adnate, distant gills on Marasmiellus sp. mushrooms follow radial symmetry. Photo: Sarah A.

Both thinkers expressed the idea that nature has an underlying, discoverable design, and that this design is not random, but mathematically coherent and deeply interconnected - giving a certain order to the chaos. 

Petal to Porpita — symmetry binds them both. Photos: Sarah A. 

Imagine you’re walking along a beach. You watch the sea trace ripples across the sand, leaving its mark — never quite the same. A few steps ahead, you spot a seashell, its surface etched with a delicate spiral. Nearby, a cluster of barnacles clings to a rock, their openings forming a rough mosaic. Under that rock an urchin is nestled in a crevice, spines radiating outward in perfect geometric order. Sand bubbler crabs busily roll tiny pellets into mandala-like patterns. In the littoral forest, there are trees branching into miniature versions of themselves. On the branches, leaves stretch outward, their veins forming intricate patterns—mirroring the refracted sunlight through the shallow water. It may seem that pattern-forming is universal in the natural world - they are found everywhere, from the microscopic to the cosmic. 

Veins on a leaf seem to merge with caustic light patterns. Photos: Sarah A. 

Radiating patterns created by sand bubbler crabs are a result of their feeding habit, maximizing the area searched for food and avoiding sifting through the same sand. Photo: Priya Mandal. 

These patterns are not imposed upon nature; they are nature. Whether through physical laws, chemical regularities, or evolutionary constraints, the world shapes and folds itself into form.

Studies at Brookhaven National Laboratory  have shown that venation patterns in dragonfly wings follow the golden angle. Photo 1,2: Sarah A. 

Many explanations and theories have emerged—and continue to evolve—in an effort to understand the ‘why’ behind these wondrous designs. 

D’Arcy Thompson, biologist and mathematician, wrote in his book On Growth and Form (1917), that “physical forces and internal growth parameters regulate biological forms”. To Thompson, by modifying growth rates or forces, one could predict the form of related species[1], whereas Charles Darwin in The Origin of Species (1859) viewed patterns as being the outcome of natural selection over time, “endless forms most beautiful and most wonderful have been, and are being, evolved”. Divergent forms arise because different populations adapt to different environments or lifestyles. [2] Convergence (similar forms in unrelated groups) arises because different lineages face similar selective pressures. [3]  Thus, where Thompson sought a mathematical common source for form, Darwin attributed commonalities to ancestry and gradual modification.

Then there is the theory of “Self Organization in Biological Structures” that has been developed over time, the key concept introduced by Ilya Prigogine. Self-organization refers to the process by which complex structures or patterns form without external guidance.[4] Perhaps a local interaction of components - such as ants following pheromone trails laid by other ants, reinforcing certain paths over time.

To the human eye - it may be coincidental beauty, but as theories suggest, it arises from function, necessity and equilibrium-seeking. An adaptive logic that has worked and will aid in survival. 

Wings of an Oakblue butterfly seen under 250x pocket microscope showing stacked chitinous scales. This vivid blue is a structural color. Photo: Sarah A.

Let’s look at some common patterns found in the physical world.

Spirals

In mathematics, a spiral is defined as a curve that winds around a central point and moves progressively further away. In natural forms this translates to expansion without altering its shape. This allows both growth and stability, especially where radial or geometric growth occurs. 

Spirals: from following the fibonacci spiral to logarithmic spirals to plain rugged geometry - there are plenty of examples in the natural world. Photos 1-3: Sarah A.

Photo 4: The Southern Pinwheel Galaxy (rotated) by CTIO/NOIRLab/DOE/NSF/AURA Image processing, Wikimedia Commons (CC BY 4.0)

Fractals 

Have you ever seen endlessly repeating patterns, where the smaller parts resemble the whole? These are fractals — a lesson in efficiency; optimizing space, flow and energy. For example, the branching of trees allows maximum sunlight capture and nutrient transport. 

Fractal patterns are most easily observed in bare tree branches. Photo: Priya Mandal. 

Lightning creates branching, self-similar structures.. Photo: Samuel John.

Walking maidenhair fern Adiantum philippense displaying a recursive pattern. Photo: Sarah A.

Symmetry and fractals in microscopic images of snowflake crystals by Wilson Bentley (1902). Photo source: Wikimedia Commons. 

Symmetry

A concept that is used quite often to understand this universe is symmetry, ideally defined as two sides of a line or central axis that are mirror-images of each other. Symmetry doesn’t ensure survival as such, though it is preferred because it’s simpler to make (less genetic information to encode).[5] 

A macro shot of a dragonfly exhibiting bilateral symmetry - the left and right sides of the body are mirror images of each other. Photo: Samuel John.

Symmetry (plate 85) in Ascidians captured vividly by Ernst Haeckel in Kunstformen der Natur (1899-1904) Photo source: Wikimedia Commons.

Urchins like this Indo-Pacific rock boring show radial symmetry. Photo: Sarah A. 

Tessellation 

A pattern that is formed from repetition of shapes that are aligned without overlaps. This favors structural stability. Take the honeycomb structure (one of the most common examples of tessellation) the hexagons are fitted together without gaps allowing efficient partition of space and minimizing usage of building materials. 

Clustered tubular egg casings of possibly a parasitoid wasp show recurring patterns that could be considered symmetrical and show tessellation. Photo: Sarah A. 

Net-like division on the surface of the cap of Hexagonia sp. resembles closely knit tiles. Photo: Sarah A. 

Biological forms - Camoflauge 

Patterns in creatures may arise from chemical interactions. A possible explanation for this was described by Alan Turing in his paper “The Chemical Basis of Morphogenesis” which showed how reactions between diffusing substances could spontaneously create complex forms.[6] In simple terms, two chemicals react and spread out at different speeds. Basically what begins as a biological murmur becomes a visible signal—then, if it helps an organism survive, a heritable motif.

The patterns on a ladybug are an example of aposematism that has evolved due to natural selection. Photo: Sarah A. 

Psychedelic patterns on the Devil Crab Zosimus aeneus are a result of aposematism and allows it to camouflage. Photo: Sarah A.

Hexagonal scales (showing tessellation) on the red-trinket snake help the snake blend into leaf litter, undergrowth, and tree bark. Photo: Nariman Vazifdar.

In stark contrast to an adult Emperor angelfish Pomacanthus imperator, the juvenile has vivid blue and white concentric swirls produced by chromatophores. This helps in camouflage, predator avoidance and social signaling. Photo: Karishma Goenka.

In the juvenile Blue triggerfish Pseudobalistes fuscus yellow geometric motifs adorn a blue background which aid in disruptive coloration and environmental blending. Photo: Karishma Goenka.

While science and logic have brought us closer to understanding the natural world, there are moments when nature defies explanation—when form, function, and beauty converge in ways we can observe but not fully grasp. Perhaps it is safe to say that nature doesn’t really plan, but she most certainly learns. 

Some images of hard coral teeming with natural patterns, for your viewing pleasure. 

Distinctive patterns on corals are multifunctional adaptations that aid in structural strength, optimize photosynthetic productivity, enhance water dynamics, prevent algal growth and aid in survival. 

Photo 1: Fluorescence of Lobophyllia  sp. coral by Karishma Goenka

Photo 2: Visually striking patterns of Mycedium sp. coral by Chetana BP

Photo 3: Ridges and valleys of Pavona sp. coral by Karishma Goenka

Photo 4: Maze- like appearance of Platygyra sp. coral by Sarah A.

Photo 5: Round, closely packed corallites of Diploastrea sp. coral by Chetana BP

Photo 6: Whorls of individual raised polyps of Galaxea sp. coral resembling starbursts by Sarah A. 

Citations

[1]Abzhanov A. The old and new faces of morphology: the legacy of D'Arcy Thompson's 'theory of transformations' and 'laws of growth'. Development. 2017 Dec 1;144(23):4284-4297. doi: 10.1242/dev.137505. PMID: 29183941. 

[2,3] Darwin, C. On the Origin of Species by Means of Natural Selection, or the Preservation of Favoured Races in the Struggle for Life. London: John Murray, 1859.

[4]Camazine, S., Deneubourg, J.-L., Franks, N. R., Sneyd, J., Theraulaz, G., & Bonabeau, E. (2001). Self-Organization in Biological Systems. Princeton University Press. ISBN: 9780691116242.

[5] Johnston, I. G., Dingle, K., Greenbury, S. F., Camargo, C. Q., Doye, J. P. K., Ahnert, S. E., & Louis, A. A. (2022). Symmetry and simplicity spontaneously emerge from the algorithmic nature of evolution. Proceedings of the National Academy of Sciences, 119(11), e2113883119. https://doi.org/10.1073/pnas.2113883119 

[6] Turing, Alan M. “The Chemical Basis of Morphogenesis.” Philosophical Transactions of the Royal Society of London. Series B, Biological Sciences, vol. 237, no. 641, 1952, pp. 37–72. https://doi.org/10.1098/rstb.1952.0012

Further reading

Ball, Philip. Patterns in Nature: Why the Natural World Looks the Way It Does. University of Chicago Press, 2016.

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About the author:

Sarah is a silly goose, who waddles through life with a microscope in one hand and a paperback in the other. She loves exploration, science, maps and swears by Lord of the Rings. 🏴‍☠️