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.
What 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.
We 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 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.
Mamma 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.
Rounded 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.
Often 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.
A 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 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.
A 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.
Equiangular 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
To 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.
A 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 bubble 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.
A star is an explosion. Many plants feature explosion shapes. Spikes on a cactus are explosions. Their spikes project outward for maximum 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.
Many 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
The 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.
Lava, 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.
As 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
Just 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.
Rarely 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.
As 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.
Sometimes 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.
Air, 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.
Rocks, 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.
When 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. From 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.
Mathematicians 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 from 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.
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.