with Lorelle and Brent VanFossen

Patterns in Nature – Lines and Shapes

The forces of nature influence our perceptions – what we see and how we see it. We may be consciously or unconsciously aware of the influence of these forces as nature can move suddenly or slowly. Nature’s forces are gravity, wind, water and geologic – like volcanic action, earthquakes, etc. Gravity is one of the most powerful forces which consciously influences our attitudes and perceptions. And nowhere is that more evident than in lines.


Vertical lines in tree trunks, photograph by Brent VanFossenWhat goes up must come down. Gravity wins. We know that whatever goes up – straight up – will eventually fall down. Vertical lines are exciting and dramatic. They rebel against gravity and soar upwards. They imply energy, strength and motion.

Horizontal lines of grasses floating on water, photograph by Brent VanFossenWe are confident in the fact that horizontal lines won’t fall down. They are already lying down. So they feel safe and give us a sense of calm. We often associate straight, smooth, flat lines and shapes with a floor, a calm sea, a flat road. It means safety, stability, yet can also become a bit boring and static – a sensation of stillness and going nowhere.

Diagonal Lines in these half falling trees give a sense of danger, of falling, photograph by Brent VanFossenDiagonal lines imply motion, moving uphill or downhill. They provide a sense of direction and perception of distance by leading the viewer’s eye into or away from the subject. Diagonal lines are often caused by storms, earthquakes and geological forces pushing and shaping the earth.

Jagged lines in the trees along a ridge, Hurricane Ridge, Olympic National Park, photograph by Brent VanFossenMamma warned you about running with the scissors. Sharp points and broken glass, we learned quickly, mean injury and pain. We are taught that jagged lines and pointed objects are things to be cautious of – even scared of. Jagged lines like mountains or hanging stalactites can create great excitement as they imply a sense of daring and threat.

Flowing curves along this leaf, photograph by Brent VanFossenRounded lines, shapes and curves project a sense of tranquility and safety, jagged edges that have been softened and rounded. They offer few surprises and flow along smooth curving surfaces. They move the eye through the image slowly as opposed to sliding in a fast motion along a straight line.

S curve found in the neck of swan, photograph by Brent VanFossenOften found in nature, S-curves are sinuous lines which move the viewer along its sensuous path slowly. They are found in shorelines, trails, rivers and pathways, and are often referred to as meanders and ripples. S-curves are so graphically strong, if an edge of the S leaves the frame, the eye will follow the curves back into the frame, tracing the shape.

Triangular trees with a dusting of snow, photograph by Brent VanFossenA triangle offers the viewer a sense of stability; it represents strength. We often associate triangles with mountains. We know that by its shape it feels secure. A mountain is certainly not going to get up and move very soon.

Helix, Archimedes Spiral and the Equiangular Spiral

A web forms an Archimedes spiral, photograph by Brent VanFossenA spiral is an even circular pattern. The Greek mathematician, Archimedes, first described what is now called the Archimedes spiral. The space between each line of the spiral and the one before and after is the same. A spider web is a good example of this spiral. After forming the “spokes” of the web, the spider moves along the center in equal distances, filling in the gaps with one continuous line.

Equiangular spiral in a sea shell, photograph by Brent VanFossenA sea shell also follows a spiral but a closer look reveals the spiral widens as it winds around itself. This was called an equiangular spiral by Rene Descartes in 1638 when he found the lines drawn from the center of the spiral intersected with the outer walls at identical angles. It is the only mathematical curve that retains the same shape while growing at only one end. The snail cannot widen the walls of its chamber but must add on to the open end of its protective shell as it grows larger.

Grape vines form helix spirals, photograph by Brent VanFossenEquiangular spirals are found in plants and animals that grow by adding identical shaped elements in steadily increasing sizes. This growth pattern creates a spiral. Lettuce, roses and other common garden plants work this way. A rose pushes the oldest petals outward as new ones unfurl in the middle.

A corkscrew curve of twisting shapes is called a Helix. In a helix, each loop of the curve is identical to the one below or above. It resembles a phone cord. Helixes are found in grapevines, some cactus, squash, cucumbers and even in DNA.

Circles, Spheres and Explosions

Circular water droplets on grass, photograph by Brent VanFossenTo the ancient Greeks, a circle and its 3-dimensional counterpart, the sphere, were considered perfect symbols of the divine. Circles represent eternity, perpetual motion, a sense of never ending stories. This symbolism is based on some realities in nature. Life begins in humans and other creatures as an egg – a sphere. The planet, sun and moon are spherical – round. Circles distribute gravity and energy uniformly.

Sphere of pitch dripping from a tree, photograph by Brent VanFossenA cat curls itself into a ball to sleep on a cold night. This creates the least surface area and minimizes heat loss. The less surface exposed to the cold air, the less heat loss. Many animals curl up in a ball for heat conservation as well as self defense – offering the least possible surface area to predators. A soap bubble, or bubble of pitch from a tree, forms a sphere for the same reasons: the least surface area for the most volume. There is a balance formed between the inward and outward forces of air in a Anename uses the explosion pattern to lead prey inside, photograph by Brent VanFossenbubble creating a tremendous amount of surface tension. Touch a bubble and it may pop.

Take a balloon, fill it with water and then drop it down on the pavement and the balloon will explode. The resulting pattern is an explosion as the water radiates out from the center in all directions. An explosion is the attempt of the sphere or circle to maintain its shape against overwhelming odds.

Cactus spikes form an explosion pattern, photograph by Lorelle VanFossenA star is an explosion. Many plants feature explosion shapes. Spikes on a cactus are explosions. Their spikes project outward for maximum Lupine Leaves with water dropslets protection of the plant’s vulnerable skin, protecting the plant from water loss by creating shade. Lupine leaves form an explosion. Combined with the fuzzy surface of the leaves, water is attracted to its surface and held there in spherical droplets, providing the most amount of water volume for the least surface area, keeping water on the plant.

The explosion pattern allows the seeds of this flower pod to be carried away by animals brushing up against it, photograph by Brent VanFossenMany flowers rely upon insects to carry pollen from one plant to another for fertilization. A radiating explosion in its pattern helps not only to direct insects to the center like a landing strip pattern, but the radiating stamens and pistols, which hold the pollen, brush against the insect for a free ride to another plant. The petals on dandelion seeds form a delicate sphere of explosion patterns. This helps to keep the seed afloat on the breeze as it travels, like a helicopter.

Hexagons/Packing and Cracking

Dried corn features the hexagon patterns of nature packing it all in tight, photograph by Brent VanFossenThe shortest path between two points is a straight line. Nature works hard to pack in as much as possible in the least amount of space. This pressure to “get it all in” can create hexagon forms and cracking to accommodate the pressure of forcing a large area down even smaller.

A bee’s honeycomb, a cob of corn, and even a group of soap bubbles, all exhibit surfaces that meet in three-way junctions at 120 degree angles. This pattern allows nature to pack the pieces into the smallest area possible.

Cracks in basalt form as it cools, photograph by Brent VanFossenLava, which sinks into the ground, cools and crystallizes quickly. As it shrinks down, it causes a lot of stress and energy with which to crack the rock forming columns of hexagon patterns, cracking in 120 degree angles. Rock cracks are formed by the pressures of the earth’s surface moving. When enough pressure forces a crack in the rock, the pressure shifts and forces in another direction and another crack forms. Many of these initial cracks will be at right angles. Unlike basalt which cools uniformly, these cracks occur over time and are subject to various pressures from many different angles.

Cracks form in the mud as it dries, Israel, photograph by Brent VanFossenAs mud shrinks and dries, it forms cracks over time; sequentially rather than concurrently. As a tree grows, its bark splits to accommodate the expansion. It doesn’t split all at the same time, so the cracks and splits occur in a variety of directions. The patterns can become very complex – almost forming puzzle pieces.

Ripples and Meanders

Stream of water slowly moves through the grasses, photograph by Brent VanFossenJust as gravity puts a perspective on lines and shapes and the pressures of the earth’s movement creates cracks, the pressures of wind and water also shape nature. Water causes sinuous curves through the ground and rocks. Wind molds sand and snow.

Meandering stream cuts through the sandy bank, photograph by Lorelle VanFossenRarely do rivers and streams run straight, unless forced by the hand of man – remember we love straight lines. Water initially pursues a course down a steep incline in a straight direction. Again, the shortest path between two points is a straight line. Yet, as the slope declines towards a flat surface, the water hunts for a path to maximize its momentum. Curves result. These are called meanders after the Maiandros river named by the Greeks for its winding course.

Water in a stream pushes against rocks, photograph by Brent VanFossenAs a river goes on along its course, it meets an immovable object. It pushes against the edge, eroding the surface. As the water hits the “corner”, it rebounds across the channel carrying away the soil it has chewed from the other bank. This process not only shapes the curves and bends of the outside of the river, but the action of the water traveling across itself causes ripples on the surface.

Small rocks grind holes in the soft sandstone, Pebble Beach, California, photograph by Brent VanFossenSometimes a pebble will catch in the crack of a rock on a beach or along a stream. The action of the water flowing over it causes it to move around, back and forth. Over time, the pebble drills a circular hole. Other pebbles may join it in its spinning and drilling processes, making the hole larger. Then plants and animals of the sea or river may find themselves a home in these protected holes. Nature creating a haven for nature.

Wind blows snow into ripples, Hurricane Ridge, Olympic National Park, photograph by Brent VanFossenAir, in many ways, acts the same as flowing water. It carries along bits of sand and silt for a distance and then deposits them somewhere else. This creates ripples in the surface of sand or snow. The harder the wind blows, the sharper and more pronounced the ripple. The slower it blows, the softer the curve – creating soft mounds.

Meandering ripples in the sand at Turnagain Arm, Alaska, photograph by Brent VanFossenRocks, branches and grasses can form patterns and ripples across sand and snow. The sense of motion is repeated over and over again. Waves, ripples and motions. The wind picks up the grains of sand and snow, blowing them over the dune and then dropping them off on the lee side as it loses momentum.


Branch of a plant, photograph by Brent VanFossenWhen you first look at a forest, it may seem to be a random tangle of branches and leaves. Continue looking and you will notice some regularity. Follow the path of the trunk of a single tree as it moves upward. Soon a branch will protrude out from the side, then another and another. A stream branches out in a braid, seeking the path of least resistance, photograph by Brent VanFossenFrom that branch will be smaller branches, and smaller, leading to twigs, and eventually to leaves.

Look at a leaf and you will find veins. In the veins you may see more branches. A tree branches to extend its leaves to grasp at the sun’s light, giving the maximum amount of surface. The branching process also helps to shed snow and withstand wind storms.

Look at a river. The rain forms puddles which overflow to form streams. One stream joins another which joins another which flows into a main river which joins another river and eventually drops off into the sea. Branching is again nature using the shortest possible line to get the greatest amount of coverage.


Cloud, photograph by Brent VanFossenMathematicians love to explain everything. But when forced to offer a geometrical solution to the cragginess of a mountain peak, the billows and whorls of a cloud, or the intricate branching of a tree, they had a tough time. In the mid 1970’s, Benoit Mandelbrot, a mathematician at IBM, developed a geometry that could analyze and quantify nature’s crags, whorls, billows and branching. He called this new branch of mathematics, fractal geometry, taking the name Is this a picture of a coast line from an airplane or the edge of a pond? Self similarity is part of the definition of a fractal. Photograph of pond edge by Brent VanFossenfrom the Latin adjective fractus, which means “fractured, fragmented or broken”. Since then, scientists have used fractals to define order in natural structures which defy analysis.

To fit into this new category of mathematics, a shape must have what Mandelbrot called self-similarity. The details must look much like the larger picture. A tree is a classic example of fractal geometry. Take a distance view of a tree. Then magnify the image. Then magnify it again. The parts of the tree are similar in shape to the tree itself.

Rock mountainsides, when you move in close, continue to be smaller examples of themselves. Clouds have the same irregularities as other natural features. Look close or look far away and feel no sensation of size. They all look like clouds.

Fractals: Self Simularity

The following images show the “self-similarity” between rocks on a mountainside from a distance and closeup. Notice the similarity even though the rocks change shape and arrangement.

Rock face, photograph by Brent VanFossenRock face closeup, photograph by Brent VanFossenBroken rocks, photograph by Brent VanFossenBroken rocks closeup, photograph by Brent VanFossen


  • hannah
    Posted June 20, 2005 at 6:17 | Permalink

    Wow! some absolutely stunning photos just great for my art project on patterns in nature!
    i love each and every one of them, you are a very skilled photographist.

  • Sioned
    Posted June 22, 2005 at 12:10 | Permalink

    Waw! amazing photos! i totally agree with Hannah (above)! these are going to be brill for my GCSE artwork! thanks! keep up the good work!

  • Posted June 22, 2005 at 12:15 | Permalink

    I’m glad this series on patterns in nature is so helpful. Remember, these images are for inspiration only. We hope they are inspiring and answer questions which help you learn more about recognizing the patterns in nature.

    There are many different types of patterns found in nature. We have a variety of articles dealing with Patterns in Nature here.

    Good luck with your projects.

  • nicola
    Posted July 29, 2005 at 18:33 | Permalink

    Wow thanks! Im doing some nice summer holiday prep work for my first A-level project on Patterns in Nature. Really inspirational! Im considering incorporating photography into the course, and I’ve got some great ideas from your work! Obviously i have to credit you for the work.. thats recoded on my course sheet. But thanks so much, i can now understand alot more about the types of patterns in nature. Thanks
    nic xx

  • Terry Briody
    Posted July 17, 2006 at 18:00 | Permalink

    Simply wonderful.
    Thank you.

  • pradnyachauhan
    Posted July 31, 2006 at 22:42 | Permalink

    I teach basic design course at College of architecture in Mumbai. I was looking for some photographs on lines in nature. I came across this site and the photos are absolutely stunning. Thanks a lot for sharing these photos with us. Also my students work on lines and grids in nature and they come up with some tangible application of these lines in built form. And this is the first page I have seen!!!
    The photographs give me the idea to introduce fractal theory to students.
    Thanks again.

  • Posted July 31, 2006 at 22:53 | Permalink

    Thank you. We are very proud of our photography and enjoy teaching our Patterns in Nature Photography Workshop, from which this is part of the class book. No matter where we travel in the world, patterns catch our eye, whether in nature or man-made subjects.

    You can find the rest of the Patterns in Nature Online Book chapters here. Thank you again. And let me know if I can be of further help with your class.

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