Seeing Nature through New Eyes: Fractals
Have you ever looked closely at the fronds of a fern, the branches of a tree, or even the jagged edges of a coastline? If so, you’ve seen fractals in action. Fractals are fascinating patterns that repeat themselves in smaller and smaller sizes, no matter how closely you look. So the next time you go out with your family exploring, try seeing nature through new eyes with fractals.
What Are Fractals?
Fractals are shapes or patterns that look similar at every level of zoom. Imagine breaking a piece of broccoli into smaller pieces. Each tiny piece looks just like the bigger one. That’s a fractal! This repeating structure is called “self-similarity.” Another cool thing about fractals is that they can be infinite. No matter how much you zoom in, the pattern keeps repeating. This is different from most shapes we see every day, like circles or squares, which don’t change when you zoom in closer.
Examples of Fractals in Nature
Fractals appear all around us in the natural world. Here are a few examples:
Tree Branches: A tree starts with a trunk, which splits into branches. Each branch splits into smaller branches, and so on. The pattern repeats itself over and over.
Snowflakes: When you look at a snowflake, you see intricate designs. If you zoom in, smaller versions of these designs appear within the larger one.
Rivers and Coastlines: Rivers and coastlines have fractal patterns because they are made of smaller and smaller streams or inlets that look like miniature versions of the whole.
Clouds: The fluffy shapes of clouds are fractals, with smaller sections of the cloud resembling the overall shape. You can learn more about clouds in this other blog post.
How Were Fractals Discovered?
The concept of fractals has been around for a long time, but the term “fractal” was first used by a mathematician named Benoît Mandelbrot in 1975. He noticed that natural shapes, like coastlines and mountains, didn’t fit into the neat lines and curves of traditional geometry.
Using computers, Mandelbrot created mathematical equations to generate fractals. One of the most famous fractals is called the Mandelbrot Set, which produces a stunning and endless design of swirls and patterns when you zoom in on it. These computer-generated fractals showed how math could describe the messy and beautiful complexity of the natural world.
Why Are They Important?
Fractals are not just beautiful; they’re also useful. Scientists use fractals to model and study weather patterns and ecosystems.
Hurricanes, for example, are giant storms with swirling clouds that form a spiral shape. This spiral is a type of fractal because the structure of the hurricane—from the large, sweeping spiral to the smaller bands of wind and rain—looks similar at different scales. They study the wind speeds, cloud shapes, and temperature changes within the hurricane. By analyzing the fractal-like patterns, they can predict how strong the storm might become, where it will move, and how quickly it might grow. This helps communities prepare for hurricanes and minimize damage. Interesting, huh?
Ants use a fractal-like strategy when they search for food. When an ant leaves the nest, it starts by walking in a straight line. If it doesn’t find food, it will begin to branch off into smaller paths, creating a pattern that looks like a tree or a network. This fractal-like search helps ants cover more ground while ensuring they don’t stray too far from the nest. When one ant finds food, it leaves a trail of chemicals called pheromones for others to follow. This creates another fractal-like pattern as more ants join the path and branch off to look for additional food nearby. By following these efficient fractal patterns, ants can gather food quickly and bring it back to the colony. Watch ants the next time you are out on a field trip. See if this behavior rings true for you.
Scientists study these behaviors to design robots and computer programs that mimic ant movement. This research helps solve problems like finding the best delivery routes or organizing information efficiently.
Take a Closer Look
So the next time you go outside, take a closer look at the world around you. Whether it’s the shape of a tree, the cracks in the sidewalk, or even a seashell, you might spot a fractal. Fractals remind us that the universe is full of repeating patterns, both big and small. Who knew math could be so beautiful? If you want to explore more, check out our Math in Nature module this month at The Field Trip Academy. Click here for more details.
