Fractal geometry can visually model what we see in nature - mountains, oceans, and beaches. Fractal geometry deals with shapes made in nature. Fractals are also used for things such as modeling soil erosion and analyzing seismic patterns. The Mandelbrot Set has revealed seemingly organic shapes including twig, leaf, flower, fish, seed, and branch shapes. These are often arranged in the midst of flows like air or water.
Fractal geometry descibes the kinds of shapes that actually occur in our organic world.
This is also true of ocean waves, the ripples on a river, the flames from a bonfire, and of all flows of liquid, air, and fire. Trees have large branches that sprout smaller branches that sprout smaller branches that sprout twigs and all of these have the forms and angles of the character of the tree. This is also true of most plants. A coastline is not only a good example of fractal geometry but of fractional dimension as well. Fractional dimension is the extra dimension that a fractal object possesses which makes it have no definite length although it occupies a finite area.