Patterns in Nature, editorial design project by our 2nd-year student Ellen Andersin.

Patterns 

In Nature 

A glimpse into the world of phenomenal 

natural patterns 

Ellen Andersin

Patterns in Nature 

When observing the incredibly 

diverse natural world, one may find it 

overwhelming and complex. However, 

the reoccurring similarities become 

more evident, the more we look. First 

we notice the pattern of daily things, 

the cycle of night and day, ocean 

waves hitting the coastline in perfect 

rhythm, and the moon and tides. But 

how is it possible the zebra’s stripes 

imitate the ripples of sand dunes? 

What we notice is that the same 

types of patterns, are often occurring 

at different places, having nothing to 

do with each other. Many patterns in 

nature follow the same self organizing, 

spontaneous processes, which 

lead to a world full of similarities. 

From sea shell spirals to galaxies, 

the mirrored symmetry of most 

animals, to the branching networks 

of blood vessels, rivers and lightning. 

Explore these remarkable patterns of 

beauty, innovative design and most 

importantly; function. 

Symmetry 01. 

Fractals 02. 

Spirals 03. 

Chaos & Flow 

Waves & Dunes 

Bubbles & Foam 

04. 

05. 

06. 

Voronoi 

07. 

Cracks 

08. 

Spots & Stripes 09.

01. 

Symmetry 

Symmetry is one of the 

main concepts modern 

physicists use to 

understand the world, 

as well as what the 

ancient philosophers 

wished for in an 

ordered universe. 

Plato imagined a world 

created with geometric 

principles, based on 

harmony, proportion 

and symmetry. 

Symmetry allows us 

to reflect, rotate or 

move something while 

remaining looking 

the same. 

1 

2 


4

The majority of animals have mirrored 

external symmetry; humans, mammals, 

fish etc. Mirrored, or also called bilateral 

symmetry is recognized when you can 

draw a hypothetical vertical line in the 

middle of the animal and both sides are 

alike. Bilateral symmetry makes it easier to 

move in a specific direction, which explains this 

popularity by animals (1, 3). Bilateral symmetry 

also exist in plants, such as their leaves but also in 

flowers like orchids. Plants, flowers and living things 

can arrange themselves in stunning symmetries. 

Some have threefold symmetry which means objects 

repeat themselves three times in a 120° axis, or 

have three “arms” or leaves. Fourfold symmetry also 

happen among plants, fruits and other living things. 

Fivefold symmetry is found in for instance sea creatures, 

like the family of echinoderms which include star fish 

(4), sea urchins and sea lilies. These however have 

evolved from bilateral symmetry, in fact their larvae 

are still bilateral. Fivefold symmetry is also 

3 

found in many flowers as well as some fruits. 

Snowflakes are an incredible example of 

sixfold symmetry. They repeat themselves 

in six arm in unique but similar shapes. 

Moving on to rotational symmetry. Think 

of jellyfish (2), it has a clear top and bottom 

but is rotationally symmetrical. If you look at it 

from the top and rotate it, it looks the same. This 

is common in plants (5) and some animals. Rotational 

symmetry is found at different scales among non-living 

things, for instance the crown-shaped splash pattern 

formed when a drop falls into water. Another example 

could be the shape and rings of a planet like Saturn. Sea 

anemones are radially symmetrical, which means their 

form is perfect since their adults do not have to move, in 

comparison to the animals with bilateral symmetry who 

move in a specific direction. The most common flowers 

feature this form as well, with a clear top, bottom, middle 

point and the petals growing in a 360° shape around. 

4 5 

5 Symmetry

02. 

Fractals 

Natural fractals may 

look very chaotic when 

you first see them; 

mountain profiles, 

trees and coastlines 

do not have any exact 

symmetry. However, 

fractals have a so 

called “hidden logic” 

to their patterns; 

hierarchical repetition 

and self-similarity at 

decreasing scales. 

1 2 


6

Looking at a picture of coastlines, clouds and river 

networks without a scale bar makes it hard to know 

if it contains meters, kilometers or hundreds of 

kilometers of information. When zooming in, the 

same shapes occur, in a self repeating manner; If you 

are shown just a bit of it, you can’t tell how much of 

the whole it represents. Therefore, a fractal is a self 

repeating pattern in different levels, that looks similar 

at any scale. The structure starts from simple shapes 

that multiply over time but keep the same pattern, 

which means it looks more complex at larger scales. 

In mathematics, fractals are infinite, but in nature 

this is not perfectly possible, so all fractal patterns in 

nature are only approximate. For instance, real objects 

are made of an actual substance and can’t get smaller 

than the atoms they are made of. Equally there is an 

upper limit, you do not get trees as big as mountains. 

Examples of Fractals occurring in nature are tree 

branches (1,3), lightning, galaxies, clouds, blood 

vessels, as well as ocean waves, coastlines, river 

3 

networks and mountains (2). Fractals in nature are 

not infinite as mentioned, so they only have a certain 

amount of levels to them. For example a Romanesco 

broccoli (5) might only have 3-4 levels of self-similarity. 

Fractal branches in biology have a useful role. The 

passages of your lungs, the networks of arteries, veins 

and capillaries in the vascular system are all fractal 

systems. Same for the networks in trees and their vein 

systems of leaves (4). These branching networks are 

the most efficient in terms of energy, whether it’s to 

transport air, blood or the sugary sap of a plant. Their 

structure makes the amount of energy needed to 

transport the fluids to all points, as small as it can be. 

4 5 

7 Fractals

03. 

Spirals 

Spirals are everywhere 

in the universe, in 

both large and small 

scales; snail shells, 

galaxies, cyclonic 

storms and plants. 

Most spirals in nature 

have a shape called 

logarithmic, which 

means that a small 

part looks just like 

the bigger part, like 

fractals. A snail shell 

that grows in this 

form can stay the same 

shape even as it gets 

even bigger. What makes 

spirals popular in 

nature then? 

1 2 


8

The most important factor to 

name is that these spirals are 

different than the spiral you get 

when you’re rolling up the garden 

hose. In that case, the width of the 

coils are the same in every turn. This 

spiral is called an Archimedean spiral and 3 

like Archemedes described it; usually comes from 

rolling up a long or flat object with a constant width. 

The natural snail shell (5) spiral becomes larger for 

every turn in a specific, logarithmic way, since its 

mathematical equation involves logarithms. What 

makes this spiral remarkable then? The shape remains 

the same no matter how small or big it is. As the 

spiral rotates into its center, it only gets narrower 

and narrower and the curvature gets tighter and 

tighter. The spiral knows no limits; it can go on curling 

inward or outward forever and remain unchanged. 

The difference with the Archemedean spiral can 

be explained with the impossibility of coiling the 

garden hose tighter than its width. 

It’s not just molluscs that feature 

the logarithmic spiral (1), so do plants 

like ferns (4), animal horns and claws, 

though these might not even complete a 

full turn. Spiral galaxies (2) such as the Milky 

Way often have logarithmic shapes, as well as 

cyclones and hurricanes. The head of a sunflower (3) is 

made up of two spirals rotating in opposite directions. 

The Fibonacci Sequence is very common in radially 

symmetrical plants. If you count the pattern of seeds 

in a sunflower, for instance, the number is equal to the 

Fibonacci Sequence. The leaflets of pine cones have the 

same structure as the sunflower, and the Romanesco 

broccoli’s florets as well. Their arrangement of leaf 

motion, or phyllotaxis, is based on the same structure, 

the Fibonacci sequence. The structure allows the 

plant to constantly grow but stay secure and strong. 

The spiral shape maximizes their sun and rainwater 

intake, while taking up the least amount of space. 

4 5 

9 Spirals

04. 

Flow 

& Chaos 

The universe is always 

on the move. From 

clouds of gas and dust; 

stars form. Water 

circulates around 

the oceans in loops, 

driven by saltiness and 

temperature differences. 

Rivers flow down from 

mountains in branching 

formations like the 

blood flows in our 

veins. Many of these 

flows are too turbulent 

and fast to be 

predictable or maintain 

a constant form. Yet 

there is still order. 

1 


10

2 3 

The fundamental forms of fluid flow, such as the 

whirpool vortex (2), can be recognized from cyclones, 

water going down the drain, as well as when you stir 

your coffee in a cup. The pattern is harder to see when 

for instance fast flowing water runs chaoticly in a river. 

To see the order in the flow more clearly, we need to 

slow it down. For instance, when water is calmly flowing 

down a smooth stream, the water runs in straight paths. 

If we then add an obstacle in the flow, let’s say a rock 

sticking up, it disturbs the smooth laminar flow. How 

it is disturbed depends on several things; the viscosity 

of the liquid (water and syrup respond differently), the 

size of the obstacle and the speed of the flow. If the flow 

is slow enough, it gently passes around the object and 

then comes together on the other side. Then, when 

the flow is a bit faster, a pair of spinning eddies appear 

behind the object. Even faster flow creates a wavy 

undulation, meaning a wavelike motion and when they 

grow, they “break” and curl over into a train of vortices. 

This phenomena is known as a Kármán vortex street 

(3), and creates zigzagging, mesmerizing patterns. 

Fluid flow can not only become a patterned 

phenomenon, but creates patterns as well by 

leaving permanent traces behind. Streams, rivers 

and oceans pick up sand, stones and sediment and 

rearranging the landscape with erosion after them. 

Meanders of rivers (1,4) are fully developed by water 

transporting sediment, with input of fluid flow and 

its speed. Since the water flows faster on the 

outside of the edge of the curving river meander, it 

erodes more, while again it flows slower on the 

inside where sediment gets collected. This 

forms the rivers to bend and curl more 

and more over time, and eventually 

two sides of the loop meet and 

merge. The stronger this 

phenomenon gets the 

4 

more complex the 

meanders get. 

11 

Chaos & Flow

05. 

Waves 

& Dunes 

In a way, most of 

nature is basically 

waves; light and sound 

are undulations, 

meaning they move in 

wave-like patterns. 

Oceans and the 

atmosphere support 

oscillations, the 

repetitive movement in 

time and, in general, 

waves are patterns in 

time, as well as space. 

It is a constant pulse, 

a periodic coming 

and going. 

1 


12

2 3 

Waves are spread throughout nature and carry 

energy as they move. Sound waves are vibrations 

of the air (4), while light is a wave of oscillating 

electrical and magnetic fields, moving through 

space faster than anything else. Colliding waves 

may reinforce or cancel out one another, depending 

on whether they are in or out of step. Interference 

of light waves may result in spectacular colors, 

like soap or oil films on water. When sound waves 

are restricted to a fixed space, like an instrument, 

certain frequencies and patterns may be picked 

out in the phenomenon of resonance. The 18th 

century scientist and musician Ernst Chladni 

discovered that it is possible to create interesting 

patterns of scattered fine grains (2), laying on 

a metal plate, only from sound wave vibrations 

when drawing a violin bow across the edge. 

Sea surface waves create a chaotic pattern on 

water, driven by wind waves. As waves in water or 

wind pass over sand, patterns of ripples appear (1), 

and if bigger, dunes are created. Different patterns 

form in dunes when the wind arranges sand grains into 

regular structures; crescents, long lines, stars, domes 

or parabolas, and they may look very different from 

another. These self organizing patterns are based on 

the particular speed of the wind and the average grain 

size. This is why dunes on other planets, let’s take Mars 

as an example (3), may also have similar dunes but form 

patterns not possible on Earth. The different conditions 

affect the ways the grains are transported and how they 

bounce; the gravity is weaker or Mars, the atmosphere 

is thinner and the winds can be much faster. 

4 

13 Waves & Dunes

06. 

Bubbles 

& Foam 

Something as playful 

as soap bubbles have 

fascinated scientists 

for a long time. 

Bubbles and foam have 

a certain charm and 

beauty to them but also 

extraordinary shapes. 

Soap bubbles hold the 

smallest possible 

surface area for the 

volume enclosed, in 

their sphere shapes. 

A mass of bubbles, or 

foam, are simply guided 

by the laws of physics 

into astonishing 

hexagonal patterns. 

1 

2 


14

3 4 

The masters of hexagons, apart from physics of 

course, are the bees with their honeycomb (1,2). They 

demonstrate precious engineering in their array 

of prism-shaped cells with a perfectly hexagonal 

cross-section. Yet this structure is made without 

any blueprint; by simultaneously working bees, 

somehow managing to be coordinated. The wax 

walls are made with precise thickness and they even 

manage to avoid mismatched cells somehow. 

The other question is; why hexagons? Because of 

geometry. If you want to pack cells together that are 

all identical in shape and size, so that they fill a flat 

surface, only three regular shapes work. They all have 

identical sides and angles and it is either equilateral 

triangles, squares or hexagons. Out of these three, the 

hexagons require the least amount of wall compared 

to the others of the same area. The bees make their 

walls from wax which require energy to produce, so 

the hexagons are the most economic choice (5). 

Foams (4) are even more concerned about economy 

than bees. The soap bubbles are made of water with 

a skin of soap molecules and the surface tension is 

constantly pulling towards a structure that holds the least 

amount of soap-film wall, meaning the smallest liquid 

surface area as possible. At the same time the structure 

has to be mechanically stable and this is part of the 

reason why you for instance never see square bubbles; if 

four bubbles would be surrounded and pressed by four 

walls, they instantly rearrange into three-wall junctions. 

This is rooted in the dominant preferences of science. 

The eyes of insects (3), with their many light-sensitive 

cells are packed hexagonally, like the foams, with only 

three cell walls meeting at each vertex. 

5 

15 

Bubbles & Foam

07. 

Voronoi 

What do giraffes, corn 

on the cob and leaf 

cells have in common? 

They all feature the 

natural pattern called 

Voronoi Tessellation. 

The pattern is based 

on efficiency, cutting 

lines to the nearest 

neighbor with the 

shortest path available 

in the tightest 

fit possible. 

1 2 


16

3 4 

The Voronoi pattern (1) is very common in the natural 

world, most fashionably worn by giraffes (4) and 

turtles (3). The dragonfly (5) shows off this irregular 

pattern in their wings, and a regular Voronoi pattern 

looks like the bees’ honeycomb. Most commonly 

the Voronoi cells are irregular, for instance in 

the case of the turtle. Your food may feature this 

pattern as well; corn on the cob as mentioned, 

pineapples, strawberries and a head of garlic. 

The Voronoi Tessellation is one sort of Tessellations 

in nature. This category features patterns build by 

repeating tiles over a flat surface. Think of reptiles, 

like snakes (2), or fish with their astonishing scales, 

they all have these protecting, overlapping scales 

and tiles. Some other animals have this pattern as 

well, like the pangolin or alligators, fruits like the 

salak and flowers as the snake’s head fritillary. 

The Voronoi pattern is build up based on its middle seed 

points. Picture a number of randomly placed dots. Each 

seed or dot has its own region, or cell, consisting of all the 

points of area that is closer to that seed than any other. 

Imagine that each seed would blow up like a bubble, all 

in the same speed. The cell walls or lines of the Voronoi 

is where the bubbles would meet 

each other. 

5 

17 

Voronoi

08. 

Cracks 

Cracks and breakage 

seem to be the absolute 

opposite of order and 

organization, but 

these patterns appear 

very often in nature. 

Therefore, the only 

possibility is that 

they also produce 

patterns and structure. 

“Geometry of failure” 

comes from things 

breaking and cracking; 

creating branching, 

jagged, forked and 

fragmented patterns. 

1 2 


18

The branching tips of cracks, split into ever more 

junctions, which means this category shows yet 

another fractal system in nature. These patterns not 

only appear in the cracking of mud (4), but can also 

be recognized in rivers’ networks. These branching 

networks have a kind of “slow crack” as they erode 

the landscape in which they form, splitting apart 

the earth and carving mountain ranges. The sea, 

as well, is constantly eroding the coastlines, with 

the energy of the water’s movement, creating 

random fractal patterns. These geological processes 

happen over decades, centuries and millennia. 

Lightning (3) has a very similar pattern to the 

branching, fractal networks. When the high voltage 

electricity travels through and splitting a material, 

a dielectric breakdown happens. What’s interesting 

is that the pattern of the lightning crack is like a 

frozen replica of the spark that started it, called the 

Lichtenberg figure. The electricity flow generally 

chooses the path wherever the electric field at the 

boundary of the discharge is the strongest, which 

usually is at the sharpest points, at bulges and tips. This 

is why lightning bolts often strike at the highest trees or 

buildings and why lightning conductors are sharp spikes; 

they encourage the electrical discharge to happen there. 

Shrinkage stress is a huge reason for cracks to appear, 

for instance when mud dries up and shrinks, cracks 

appear where the stress is the strongest. The same 

happened in the case of the Giant’s Causeway (2), where 

instead of mud it’s magma that cooled down, shrank 

and cracked. The islands of these patterns usually have 

a polygonal shape, even though in most cases they can 

be less smooth and inconsistent (1). However, in the 

case of the Giant’s Causeway, with its highly regular, 

almost geometric shapes, it is hard to believe this is 

from the same process. When cracks grow downward 

in a thick layer of mass, the cracks tend to break up 

into prism shaped columns with the pattern getting 

more organized, the deeper the cracks get. Additionally, 

about 60 millions of years of erosion has removed the 

uneven, top layers of the Giant’s Causeway, exposing 

only the striking, honeycomb-like, natural pattern. 

3 4 

19 Cracks

09. 

Spots 

& Stripes 

Animals have the most 

incredible designs of 

patterns, and one may 

wonder how and why they 

are this way. It is one 

thing to discuss why; 

it may be a process 

of natural selection 

and camouflage, but 

what scientists have 

struggled to explain 

is how these markings 

appear. In the end, 

it has more to 

do with mathematics 

than biology. 

1 2 


20

3 4 

All kinds of innovative patterns are worn by animals, 

but they do seem to follow certain trends. The stripe 

pattern of the zebra (1) surely is a popular one, 

with some fish, tigers, antelopes, caterpillars and 

frogs wearing the same markings. Spots are also 

seen widely in the animal world, like on leopards, 

ladybirds, fish and insects. The reasons for these 

patterns may be as warning signs for predators, 

or as a tool to recognize members of the same 

species. Camouflage is a popular feature, to fade 

as well into the surroundings as possible, or the 

opposite; to attract and impress the opposite sex for 

mating, like the peacock’s striking tail feathers (3). 

Now the question is, how does the embryo of a zebra 

get imprinted with these stripes? How does the 

pigment producing skin cells organize and design 

which part that should be dark or light? The widely 

accepted explanation by scientists is that these 

patterns are an outcome of a self-organizing process 

also seen in many different natural pattern making 

phenomena. It was the mathematician Alan Turning 

who came up with the formula. He watched the 

process of embryos and found that it was chemicals 

that moved across the embryo that formed these 

patterns. The principle is that the process requires both 

activator and inhibitor chemicals and in the simplest 

case, zebra stripes are born. With these two ingredients 

you can make almost endless amounts of patterns, 

sometimes needing an extra ingredient in the mix. So 

while the pelt pigmentation of tigers, leopards, zebras, 

giraffes and more come in many different patterns, 

they all come from the same biochemical process. 

The mesmerizing patterns of bird feathers are usually 

continuous, and the colors are actually 

established before the feathers get 

divided up into separate barbs. 

Reptiles and amphibians are also 

known for their markings, colorful 

patterns and even pointillist patterns like the 

chameleon (2). The reptiles with scales actually 

have similar, very geometric patterns underneath 

the top layer too. Butterflies seem to have no limits, 

sporting stripes, dots and elements like eye spots 

and outlinings of veins. Fish and sea creatures (5) 

also have incredible markings of spots and stripes, 

but in even more stunning, bright colors (4). 

5 

21 Spots & Stripes

Credits 

While the text is written 

by Ellen Andersin, a huge 

source of inspiration and 

access to information was 

the book Patterns In Nature, 

by Philip Ball (Chicago and 

London: The University of 

Chicago Press, 2016). Another 

great source of information 

was the ECstep’s website 

on “Natural Patterns”. 

To make this project possible 

and visually striking; 

sincere gratitude to the 

many photographers and 

users on Unsplash, Flickr, 

Pexels and Pixabay. 

Graphic Design by 

Ellen Andersin 

2021 


22

This book explores the diverse and innovative 

designs of nature, with the different types of 

natural patterning processes happening around us. 

With breathtaking pictures, we take a look at how 

the zebra paints its coat, why the trees branch 

like rivers, and how the spirals of sea shells 

are similar to galaxies and plants. 


24

Patterns in Nature, editorial design project by our 2nd-year student Ellen Andersin.

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