In the simplest form of this sequence, each number is the sum of the previous two: 1, 1, 2, 3, 5, 8, 13, 21 . . . .Fibonacci numbers can be used to characterize certain properties in nature, such as the spiral patterns in the heads of sunflowers. Nature has arranged sunflower seeds without gaps in the most efficient way by forming two spirals. The ratio of these spirals varies from one kind of sunflower to another. A similar double spiral occurs in the Norway Spruce cone with a ratio of 5 scales in one direction and 3 in the other. The pattern of the common larch is 8 to 5, and of the American larch, 5 to 3.
The musical scale is based upon the ratios of 1:2, 1:3, 1:4, etc. The Parthenon of ancient Greece is designed with these very ratios, which are pleasing to the eye and to the ear. The division of the conch shell and the spiral of the snail shell display the same ratios. This progression of ratios can be illustrated as an extension of the Fibonacci sequence.
We recognize a butterfly by its distinctive colors and patterns. The patterns of the giraffe, tiger, fish, or spider's web are unique to that species. Although individuals within the species may vary, each spider builds its web according to the pattern of its species.
A fractal is a type of curve which has some feature repeated on a different scale, such as the pattern of a coastline. Each kind of tree has its own unique pattern of branching, as do a lilac bush, or a ragweed plant, or other similar shrubs.