Google DeepDream Elaborated
The idea of DeepDream is this: pick some layer from the network (usually a convolutional layer), pass the starting image through the network to extract features at the chosen layer, set the gradient at that layer equal to the activations themselves, and then backpropagate to the image. 

Why does it make sense? Intuitively, it amplifies the features that are maximally activated in the network. By backpropagating this gradient, we'll make an image update that will boost any of the existing activations. If there's a cat-like detector in the layer and the image contains some patch that looks a bit like a cat, DeepDream boosts this activation by updating this patch to be even more cat-like. As a result, DeepDream is trying to find cats and dogs everywhere in the image (ImageNet dataset has lots of dogs, so the network has many dog-related neurons).

If you look at the code, the key part is objective_L2 function that makes this: $dx = x$ and then backpropagates.