  Solutions to the Einstein equations for Bianchi IX cosmologies are examined
through the use of Ellis MacCallum Wainwright (expansion-normalized) variables.
Using an iterative map derived from the Einstein equations one can construct an
infinite number of periodic solutions. The simplest periodic solutions consist
of 3-cycles. It is shown that for 3-cycles the time series of the logarithms of
the expansion-normalized spatial curvature components vs normalized time (which
is runs backwards towards the initial singularity), generates a set of
self-similar golden rectangles. In addition the golden ratio appears in other
aspects of the same time series representation.
