How to Spot a Fractal: Unlocking the Key to Finding the Fractals all around us
In this post, we’ll learn how to identify fractals in the world around us and explore the Mandelbrot fractal set through an open-source browser tool.
Jump to:
WHAT ARE FRACTALS?
Fractals are one of the most fascinating and ubiquitous concepts in mathematics and the natural world. Essentially, a fractal is a complex pattern that is self-similar, meaning it looks approximately the same at any scale. If you zoom in on a part of a fractal, it will look like the whole thing, just smaller. This property is known as scale invariance.
SPOTTING A FRACTAL
The key to spotting fractals is in its self-similarity. This is the defining feature. The structure is composed of smaller copies of itself. Take broccoli, for example. The entire head is made up of smaller florets, which each maintain the same structure as the larger head.
Once you know what to look for, you’ll start seeing fractals everywhere—in nature, art, and technology. They represent a fundamental geometry of chaos and complexity.
TYPES OF FRACTALS
Fractals aren’t just one single shape; they come in a few fundamental varieties based on how their self-similarity is generated:
Geometric Fractals (Iterated Function Systems – IFS)
These are the most visually recognizable and “perfectly” self-similar fractals. They’re built through a process of iteration, where a simple rule is repeatedly applied to a starting shape.
Algebraic or Escape-Time Fractals
These are generated by plugging coordinates into a single, simple mathematical equation and seeing what happens after many repetitions (iterations). The color of each point on the resulting image depends on how fast the numbers “escape” to infinity. Algebraic Fractals are the structures artist Julius Horsthuis explores in Fractal Worlds, currently on view at ARTECHOUSE Houston.
Random/Natural Fractals
These describe the complex, chaotic structures found in the real world. Unlike the previous two types, they are not perfectly mathematical but display statistical self-similarity—meaning the smaller parts look statistically similar to the whole.
Examples: Coastlines, clouds ☁️, lightning strikes, mountains, the branching of trees 🌳, and the structure of broccoli.
Fly through Fractals
The browser tool below lets you explore the Mandelbrot fractal set.
How it works:
- Click and drag your mouse to zoom into the fractal set
- Scroll down on the window to “reset” and play around more or “capture” your fractal creation!
FRACTAL WORLDS
WALK THROUGH FRACTALS
AT ARTECHOUSE Houston
Fractal Worlds by Julius Horsthuis is the largest fractal art exhibition ever. Across 26,000 square feet and dozens of installations, the exhibition takes you on an educational, interactive, and inspirational journey through fractals.
Over the course of your visit, you’ll learn about different types of fractals, manipulate them yourselves, and experience the potential of fractal art through the immersive cinematic centerpiece Geometric Properties.
