Fractals

A fractal is a shape that repeats itself at every size. If you zoom in on a fractal, you see the same pattern over and over again, getting smaller and smaller. Fractals are found in nature and in math.

Self-Similarity

The key idea of fractals is self-similarity. This means a small part looks like the whole thing. Think of a tree. A big branch looks like a small tree. A smaller branch looks like an even smaller tree. This repeating pattern is fractal-like.

Mathematicians create fractals using rules that repeat forever. The Sierpinski triangle starts with a triangle, removes the middle, and repeats. Each step creates more and more tiny triangles.

Fractals in Nature

Nature is full of fractals. Coastlines are jagged at every scale. Fern leaves have tiny leaflets that look like the whole leaf. Lightning bolts branch into smaller and smaller forks.

Even your lungs are fractal-like. They branch into smaller and smaller tubes to fit a huge surface area inside your chest. Fractals help nature pack a lot into a small space.

Fun Facts

• The word fractal was invented by Benoit Mandelbrot in 1975.
• The Mandelbrot set is a famous fractal made with computers that creates stunning colorful images.
• Broccoli and cauliflower are natural fractals because the small florets look like the whole vegetable.

Did You Know?

The coastline of Britain gets longer the more closely you measure it! This is called the coastline paradox, and it is a fractal property. Smaller rulers measure more tiny bumps and curves.