  From the geometric study of the elementary cell of hexagonal circle packings
--- a flower of 7 circles --- the class of conformally symmetric circle
packings is defined. Up to Moebius transformations, this class is a three
parameter family, that contains the famous Doyle spirals as a special case. The
solutions are given explicitly. It is shown, that these circle packings can be
viewed as discretizations of the quotient of two Airy functions.
  There is an interactive version of this paper that contains JAVA applets that
let you experiment with the circle packings directly. It is available at
http://www-sfb288.math.tu-berlin.de/Publications/online/
