Mandelbrot had created his own set of fractals, which are now called the Mandelbrot set, for obvious reasons. They resemble a snow man, with knobby protrusions extending from all around. When one zooms in for a closer look at the snowman, one finds that even at smaller scales, the snowman appears, though somewhat distorted. It is true that when viewed at smaller scales the Mandelbrot set becomes fuzzy, and distorted, but the ubiquitous snowman makes his appearance. Chaos and fractals are prevalent in nature.
Weather is a perfect example of chaos, and clouds make wonderful fractals.
Ferns are examples of fractals, being self-similar. Each branch of the fern is similar to the whole. One example of a fractal is Brownian motion. It is the type of motion exhibited by particles in a hot liquid, such as coffee. The particle moves with a zig-zag, random pattern, which can be plotted on a plane.