What patterns might we discern from this map?
As mentioned, Cruz was strong in the urban and especially the suburban areas, in addition to most of the border counties. The pattern as it pertains to the vast array of the rural, non-border counties is a bit more unclear... perhaps it's related to turnout? The Panhandle and that cluster in the center of the state voted mostly for Dewhurst in the first round, so there could be some significance there. Nevertheless, it's interesting to note that Dewhurst won each of the ten counties with the highest turnout...
... and Cruz won each of the ten counties with the lowest turnout (not nearly as noteworthy after taking into account just how low turnout was here; three people voted in Presidio County. But of course, most of these counties were not exactly expected to have many show up to vote in a Republican runoff.):
Just to visualize where these particular counties are (green is highest turnout, red is lowest):
I'll probably look into this more deeply later, just to see if this was even barely illuminating.