The Fibonacci progression follows this pattern: 1, 1, 2, 3, 5, 8, 13,... of which the first two items are 1 and 1 and each succeeding term is the sum of the two immediately preceding.
You will see it showing up all over in nature including in rhythms of the human body. It is represented visually by the curve of the chambered nautilus. There are many theories for how the important the progression is to human behavior, etc.
Doing a quick check on the Internet should provide interesting mullings.
