I did the sparse autoencoder exercise from here:
http://ufldl.stanford.edu/wiki/index....
After that, I got creative:
I "zapped" it with a random input (the blue trace, pink at start), and kept feeding its output back in, until it settles (red input and green output become yellow together).
Makes for some fun/trippy visualizations, and might give you insights about what your autoencoder can and cannot encode.
Try it yourself. I highly recommend it.