We have established that the generator learns how to forge data. This means that it learns how to create new synthetic data which is created by the network and looks real and created by humans. Before going into details about the GAN code, I'd like to share the results of a recent paper (code is available online https://github.com/hanzhanggit/StackGAN ) in which a GAN was used to synthesize forged images starting with a text description. The results were impressive. The first column is the real image in the test set and all the other columns are the images generated from the same text description in Stage-I and Stage-II of StackGAN. More examples are available on YouTube (https://www.youtube.com/watch?v=SuRyL5vhCIM&feature=youtu.be):

Now let us see how a GAN can learn to forge the MNIST dataset. In this case, it is a combination of GAN and ConvNets used for the generator and the discriminator networks. In the beginning, the generator creates nothing understandable, but after a few iterations, synthetic forged numbers are progressively clearer and clearer. In the following figure, the panels are ordered by increasing training epochs and you can see the quality improvement among the panels:

One of the coolest uses of GAN is doing arithmetics on faces in the generator's vector Z. In other words, if we stay in the space of synthetic forged images, it is possible to see things like this: [smiling woman] - [neutral woman] + [neutral man] = [smiling man], or like this: [man with glasses] - [man without glasses] + [woman without glasses] = [woman with glasses]. The following figure was taken from: Unsupervised Representation Learning with Deep Convolutional Generative Adversarial Networks, Alec Radford, Luke Metz, Soumith Chintala, 2016, https://arxiv.org/abs/1511.06434