Fractals in Nature: How Sand and Ice Patterns Teach Us Something Extraordinary About the World

Sand patterns on a beach and ice crystals on a car windshield: nature creates magical fractal patterns everywhere, teaching us something extraordinary about the world. This is perfectly illustrated by two photos I captured: one on a beach in Portugal and the other on a frosty windshield in Utrecht. Both reveal how everything in nature is deeply connected.

From Sand Patterns to Ice Crystals: How Nature Creates Fractals

In September 2023, I spotted a sand pattern that reminded me of a tree or river delta during a walk on a beach in Portugal. It felt magical to see such a perfect detail created by retreating water. A few months later, I discovered a similar pattern on my car windshield on a winter morning in Utrecht. Ice crystals had formed the same branch-like structures I saw on the beach. The detail, the colors, and the striking resemblance blew me away. It’s fascinating how such different conditions can create such similar results!

The Science Behind Sand and Ice Patterns: What Are Fractals?

The patterns I captured both fall under a phenomenon called ‘dendritic growth’. This process occurs when natural forces like flowing water or freezing ice branch out to follow the path of least resistance. Here’s a brief explanation of these processes:

1. Sand Patterns on the Beach
These shapes in the sand are created by retreating water carrying sand particles. The speed and direction of the water flow form tree-like patterns, much like how rivers branch into a delta.

These patterns are fractals, a mathematical concept where structures repeat themselves on different scales.

Read more: What Are Fractals, and How Do They Appear in Nature.

2. Ice Crystals on Windshields
Patterns on a windshield form when water vapor freezes on a cold surface. This occurs through a process called *nucleation*, where small ice crystals form around imperfections on the glass and branch out as water molecules in the air freeze.

Photo by Michiel de Gooijer

These branching structures follow the same principles as trees or sand patterns.

Read more: The Science Behind Ice Crystals

3. Why Do They Look Like Trees?
Both sand and ice patterns follow a fractal logic, where energy or matter is distributed efficiently. This explains why the structures resemble trees: trees are designed to distribute water, nutrients, and light optimally. Nature uses the same principles everywhere.

Read more: The Role of Fractals in Natural Processes

What Sand and Ice Teach Us About the Hidden Logic of Nature

Nature constantly shows us how ingenious and beautiful it is. These patterns, which we see everywhere—from river deltas to blood vessels and snowflakes—are evidence of the power and elegance of natural processes. They remind us of how deeply interconnected everything in nature is.

But perhaps most importantly, nature invites us to pause and marvel. Like children, if we take the time to truly observe, we’ll find something extraordinary everywhere. As I’ve experienced, these moments can be utterly overwhelming and joyful.

Why Natural Patterns Continue to Amaze Us

I want people to see that nature is a true wonder. My message is simple: *Appreciate the wonders of nature.* Look closely, and you’ll find beauty in the smallest things. This aligns perfectly with my work at BrightVibes, where we tell stories highlighting how beautiful and hopeful the world is. Sometimes, it’s just a matter of slowing down and opening your eyes.

Be Inspired by the Magic of Sand and Ice Patterns

Next time you’re outside—whether on a beach or gazing at a frosty windshield—take a moment to pause. Look closely and let yourself be inspired by the magic of nature. As my photos show, beauty is all around us—you just have to notice it. And one of the ways to do this, is to make sure that you keep your inner child alive and kicking. Read here how to do just that.

All images are copyrighted to Michiel de Gooijer.