### Leon M. Lederman Science Education
Center

Prairie Resources - Exhibit Home

Regular
patterns defined by mathematicians occur throughout nature. The
atoms in a crystal are arranged in a pattern, as are the atoms
in the DNA molecule, the stripes on an angelfish, the movement
of the legs of a centipede. These patterns help to identify and
determine the characteristics of a species.
**Fibonacci Sequence**.

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.

**Fractals**

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.