TITLE: What is the equation to evenly distribute circles in a spiral?
QUESTION [6 upvotes]: What is the equation to evenly distribute circles in a spiral?  I have attached a picture to show what I am trying to achieve and need to know what the equation is for this.

REPLY [2 votes]: This packing is diagram 5(b) on the fifth page of Stephenson   and is attributed to Doyle. However, Peter Doyle. Hmmm. Well, Doyle spirals are discussed at length in the BOOK 
Evidently the most detail is in the article mentioned in Hexagonal circle packings in the plane
with the article being http://link.springer.com/article/10.1007/BF01263534?no-access=true  Beardon, Dubejko, Stephenson, Spiral hexagonal circle packings in the plane, Geometriae Dedicata, January 1994, Volume 49, issue 1, pages 39-70