CONCLUSION

Though I did not have time to do an exhaustive study, clearly the network 
appeared to train as expected, usually after about 5 cycles (240 patterns).

The first pattern, three clusters linearly distributed, appear on the 
resultant 5 x 5 grid pretty much as anticipated, with most A, B and C data 
points grouped together.  They approximate a two-dimensional distribution 
similar to the linear distribution on the unit sphere as indicated by the 
selected ideal data points.  This result was evident almost completely by
the 5th cycle.

The second pattern, three clusters in a triangular pattern, show up on the 
resultant grid generally in three clumps, as expected.  Though more testing 
is called for, the small sample shown suggests that it may take longer to 
learn this pattern than the first.

The third pattern, four clusters linearly distributed, is reflected clearly 
in the resultant grid by the 12th iteration.  The 30th iteration interestingly 
looks less "correct" than the 12th; I'd like to try varying the parameters 
to see if I can understand this further. Is this an aberration, or is there
an error somewhere?

The fourth pattern, four clusters not coplanar, shows up on the grid as the 
four data points grouped together, perhaps in a square-like pattern.  I'm not 
exactly sure what this should look like (I thought maybe they would not 
converge at all, but this is not the case), but this result does not seem 
surprising.

It would be interesting to try the simulation again using a larger grid size,
as well as trying other iteration counts and different "fuzz factors."

The program reduces the learning rate (both alpha and beta values, for the 
"winner" and its neighbors) over time.  These factors could also be adjusted 
experimentally, and further tests run.

I was pleased that in the short amount of time available I was able to achieve 
such coherent results.  With more time to tune the model I would have more 
confidence in concluding that the simulation behaves as expected.