Digital Arts Magazine has published a very good tutorial titled Creating art using the golden ratio. Using the golden rectangle (a rectangle shaped according to the golden ratio) as the canvas the tutorial divided the space into “golden sections” which becomes a spiral.

Not mentioned in the article but related is that the math behind this is based on a the Fibonacci sequence. Yep, that series of numbers that got our hero and heroine excited in the Da Vinci Code.
If you want to explore the Golden ratio and the Fibonacci spiral further check out Wikipedia there is a good article
Image credit: file from the Wikimedia Commons.