I created these visualizations of the output from a neural network algorithm for embedding a complex perceptrual space in two dimensions. It would be very interesting to apply this algorithm to other visual data sets. If applied to auditory patches it could also be a useful generator of electronic music.
I had a mildly disheartening realization earlier today: this network was only able to create a map with smooth variation between written digits because the training set included ambiguous or intermediate examples. At the moment I can't think of a way to get a smoothly varying map if say, all we have is ten perfect digits. There ought to be a way though.