Finished running 4 diff simulations: 2 with 30 degree rotations, with and without integration of training examples across 2nd layer of network.  Signifiicant difference between 30 degree and 0 degrees as to training and test error.  This is understandable: 30 degrees puts most of the differentiating information into one of the 2 input variables.

Separately, and most important, is the fact that, for both rotations, the test error was significantly better for Proj4.