Google's Deep Dreamer
Google's Deep Dream project is research being done to visualize neural networks' learning to understand more about them.

First, you have to understand a Deep Belief Network on a high level. In short, it's a way for machines to 'learn' about data (images, in this case). That works, essentially, by transforming an input by several matrices (layers) through the network to get an output. Deep Belief Networks are trained to reconstruct their original image. All of the images are generally of some type, like animals. After some training, they begin to recognize basic features that are common between members of the training set, such as edges or colors.

The images published for the Deep Dream project are different ways of visualizing the data from trained networks. For some of the images, they observe the state of the image in layers between the input and output, resulting in artistic looking sketches of the original. For other images, they start with one image that is not related to the training set, send it through the network, then send the output through the network repeatedly to accentuate features that the network found in the image.