I don't get it. If you trained to recognize black and white, why did it find such a complex pattern where there were clearly none in the first example? Isn't it an example that it failed?
The complex pattern is a result of the network doing the equivalent of fitting 3 gaussians (1 for each of RGB color channel) on the intensity of the pixel in that channel. I was curious, so I recorded a tiny demo of doing the equivalent piecewise in photoshop: http://cl.ly/183Z3w1V1B0F
Posterization in photoshop is a k-means technique, and each k-mean is a center of a gaussian, hence my motivation for the analogue video.
The triangles in the thresholded image make me think that the network is doing the equivalent of predicting a probability that a certain pixel is white/black per channel, and then these channels collude for the final decision, and thus we see triangles when the intersections of the 3 triangly spaced gaussians yield a value above some threshold.
Pic of the different channels: http://cl.ly/image/1w371V3U0N02