Fractals in Nature
Once the basic concept of a Fractal is understood, it is shocking to see how many unique types of Fractals exist in nature. Some of the most common examples of Fractals in nature would include branches of trees, animal circulatory systems, snowflakes, lightning and electricity, plants and leaves, geographic terrain and river systems, clouds, crystals.
Fractals are seen in the branches of trees from the way a tree grows limbs. The main trunk of the tree is the origin point for the Fractal and each set of branches that grow off of that main trunk subsequently have their own branches that continue to grow and have branches of their own. Eventually the branches become small enough they become twigs, and these twigs will eventually grow into bigger branches and have twigs of their own. This cycle creates an “infinite” pattern of tree branches. Each branch of the tree resembles a smaller scale version of the whole shape.
Fractals in Animal Bodies
Another incredible place where Fractals are seen is in the circulatory and respiratory system of animals. If you take the human respiratory system, you will see a Fractal that begins with a single trunk (similar to the tree) that branches off and expands into a much more fine grained network of cavities.
We’ve all heard that every snowflake is unique and one of the contributing factors to the uniqueness of snowflakes is that they form in Fractal patterns which can allow for incredible amounts of detail and also variation. In the case of ice crystal formations, the starting point of the Fractal is in the center and the shape expands outward in all directions. As the crystal expands, the Fractal structures are formed in each direction. Just like the other examples of Fractals we have shared above, each iteration of the shape gets smaller and more detailed, which also contributes to the overall complexity of the shape.
Fractal Lightning and Electricity
If you’ve ever watched a lightning storm, you’re getting a front row show to one of nature’s most powerful displays of Fractals. When electricity passes through a medium that does not conduct electricity well (like air) the pattern that is created becomes Fractal. The reason this phenomenon forms is because of how the electricity interacts with the air. As the current passes through the air, it becomes superheated. Superheating of the air changes its electrical conductivity and allows the current to fragment out. This process repeats for each level of fragmentation and soon you get a Fractal. You’ll notice that if you invert an image of a lightning strike or electrical discharge, you’ll see great resemblance to a tree. This is because both are Fractals.
Fractals in Plants and Leaves
Next time you eat a salad, a pineapple, broccoli, or a handful of other foods, you are actually eating a Fractal! Plants and leaves, just like animals, have internal structures that distribute nutrients through a network of Fractals. These structures allow for easy distribution of liquids and other life sustaining materials to travel through the plant and support the life of every cell.
Beyond the cellular level, some types of plants themselves are very Fractal in look. One of the most notable examples is a type of broccoli called Romanesco broccoli. This type of broccoli has an incredible structure of spires which emanate from a single source (similar to the Fractal Snowflake) that in turn have their own spires which continue on to the tip of the plant.
A fern is another great example of a Fractal. Ferns are essentially made up of the same general structure repeated over and over again.
Fractals in Geography, Rivers, and Terrain
Much like Lightning, Trees, and Plants, Geography, Rivers, and Terrain also often fall under the Fractal category. If you think about how terrain is formed and weathered, a good part of the landscape can be attributed to water erosion. Similar to the networks that distribute fluids throughout an organism, rivers and other bodies of water collect, move, and distribute water throughout a landscape. A great example of this could be the journey water takes as it moves from a stream, to a river, to a lake or another large body of water.
As rivers and other bodies of water are formed, they are also carving out the geographic landscape which makes the land the bodies of water travel on Fractals as well. A great example of how Fractal geometry impacts geography comes in the form of measuring a coastline. If you measure a coastline with a mile long ruler, you will be able to get a very rough estimate as to how long the coast line is, but you will not be able to capture any of the finer detail like bumps, ridges, and outcroppings. However, if you shrink your ruler down to a yard, you are suddenly able to capture much more fine detail, because your instrument for measurement is much more precise. Each time you increase the granularity of your measurement, you are able to increase the accuracy of your measurement, which in the case of a coastline will increase the perimeter, because you will be able to capture more of those fine details. Because coastlines have Fractal geometry, the detail is extremely fine and will result in a very large perimeter.
Another way to think about modeling coastline geometry would be to think about the challenge of creating the outline if you are forced to use a set of cubes. To get any accurate detail the cubes must be very small, otherwise detail will be lost. You could also equate this challenge to the resolution of an image. If you have a low resolution image the pixels are very big which makes the image blurry and hard to see. As you increase the resolution of the image, the pixels get smaller, and the image becomes more detailed.
Fractals in Clouds
Clouds also display characteristics of Fractals. The turbulence that is found within the atmosphere has an interesting impact in the way water particles interact with each other. Turbulence is Fractal in nature and therefore has a direct impact on the formation and visual look of clouds.The amount of condensation, ice crystals, and precipitation expelled from the clouds all impacts the state of the cloud and the system’s structure and therefore the turbulence.
Fractals in Crystals
Like ice formations, other natural forms of crystals like those created from minerals can also exhibit Fractal properties. Depending on the specific formation of crystal and the minerals used some are more fractal in appearance than others. A great example of this would be the cubic nature of some formations of Amethyst or pyrite.
For more information on Fractals in Nature, we recommend you explore Beniot Mandelbrot’s iconic book The Fractal Geometry of Nature, which pioneered these ideas.