  In studying the formation of topological defects, it is conventional to
assume the ``geodesic rule'' which is equivalent to minimizing gradients of the
order parameter. This assumption has been called into question in
field-theoretic studies of first order phase transitions and in the case of
local defects. We present a scheme for numerically investigating the formation
of strings without assuming the geodesic rule. Our results show that the
fraction of string in infinite strings grows as we deviate from the geodesic
rule.
