I wonder how easy it would be to generate more logos like these, via neural network or other means.
Neural networks might be tricky. Logos tend to be precise, neural networks work better when the result is fuzzier. On the other hand, identifying a good logo is the sort of fuzzy problem that you might be able to train a network for. Use it as a fitness function over some other algorithm. You could have a generator that combined a variety of operations into a 'logo expression' that generates an image. Have values and…
Genetic programming using a design grammar (i.e. a hierarchical rule system, like a language grammar) is probably a much more natural fit than neural networks for generating the logos. It's been done before with other domains, including architecture. Using a neural network to learn the evaluation function (i.e. put a number on how 'good' a candidate logo is) in a GP is very possible though.