Update: after playing with this for way too long, I've found that it can converge to a spiral with 3 or 2 or even just 1 node in the 2nd hidden layer.
The 1 node case is especially interesting, because when it converges the single node must learn the whole spiral pattern. Although with noise it can be less reliable with more jagged edges, as well as take longer to converge (also bumped the learning rate down), seeing the spiral encoded directly in the 2nd hidden layer is more interesting to me.
