Fibonacci spiral is a line, which is created by drawing arcs connecting the oppposite corners of the squares in Fibonacci tiling, which is constructed of squares whose sides are successive Fibonacci numbers in length.
Fibonacci spiral exists in many objects of wildlife. It's one ob the basic curve, which you can see in small shells of nautilus and even in spirals of galaxies.
Arrangement of seeds in sunflower is an example of Fibonacci spiral among plants.
Hurricane is one of the most destructive power on Earth.
You can see Fibonacci spiral even in shapes of galaxies. Ivars Peterson in his article Sea Shell Spirals proved this fact. Nevertheless, Nautilus shell is one of examples of fractals in nature.
Fibonacci spiral inspired some artist to use it in their artworks. Below you can see an artwork by Petar Milivojevic named Gaia's gift.