The Fibonacci spiral is created by drawing arcs connecting the opposite corners of squares in the Fibonacci tiling. This spiral approximates the golden spiral, which grows by a factor of φ for every quarter turn.
The shell of a nautilus is a perfect example of the golden spiral in nature. As the nautilus grows, it creates new, larger chambers in its shell that follow the logarithmic spiral pattern with a growth factor close to φ.
Sunflower seeds are arranged in a pattern of interconnecting spirals, with the number of spirals being consecutive Fibonacci numbers. This arrangement maximizes the number of seeds that can fit in the flower head.
Many spiral galaxies exhibit arms that approximate logarithmic spirals with various growth factors. The golden ratio can be observed in the structure of galaxies like the Milky Way.
Phyllotaxis, the arrangement of leaves around a plant stem, often follows the golden angle (approximately 137.5°), which is derived from the golden ratio. This arrangement ensures optimal exposure to sunlight.