"Infinite Self-Similarity"
Clouds are not spheres, mountains are not cones, and coastlines are not circles. Nature is rough and irregular. Benoit Mandelbrot coined the term Fractal to describe shapes that exhibit self-similarity. This means if you zoom in on a small part, it looks like the whole. A fern leaf is made of smaller fern leaves, which are made of even smaller ones.
The most famous fractal is generated by the simple equation `z = z² + c`. When plotted, it reveals an infinitely complex boundary. No matter how deep you zoom, new, intricate patterns emerge. It is often called the "fingerprint of God" due to its infinite beauty from simple order.
Fractals are used in computer graphics to create realistic landscapes and textures. They are also used in compact antennas for cell phones (fractal antennas) to receive multiple frequencies, and in analyzing heartbeat rhythms and stock market fluctuations.