Understanding Fractals: How These Complex Patterns Shed Light on our World

You've almost certainly seen computer-generated fractals. Fractals are beautiful, whimsical images with colorful, intricate structures that repeat endlessly as you go down the rabbit hole. Formally speaking, a fractal is an infinitely complex pattern that is self-similar across a variety of scales. However, fractals, reflecting their geometric structure, can help us understand the world more deeply on many different levels.

Let's start with the familiar fractals of nature. “They're all around us in the trees, in the mountains, in the deltas,” he says. dave feldman at Atlantic University in Bar Harbor, Maine. Such ubiquity makes sense when you consider how fractals are created. “You can create fractals through simple iterative processes, repeated folding and branching,” he says.

However, these forms are not just for viewing. Fractals inside the lungs There's a reason for that. Such an arrangement packs a huge surface area into a small space. In this way, evolution solved the problem of maximizing the area of ​​tissue that can absorb oxygen.

But what makes fractals so puzzling is why they fascinate mathematicians, especially as a place to play and explore numbers. Here we encounter the fractal dimension. In our everyday world, a straight line is one-dimensional, a square or rectangle is two-dimensional, and a cube or sphere is three-dimensional. However, fractal structures have dimensions between these values. Although almost impossible to visualize, you can think of these as a measure of the complexity contained in the fractal.