  Humans can only interact with part of the surrounding environment due to
biological restrictions. Therefore, we learn to reason the spatial
relationships across a series of observations to piece together the surrounding
environment. Inspired by such behavior and the fact that machines also have
computational constraints, we propose \underline{CO}nditional
\underline{CO}ordinate GAN (COCO-GAN) of which the generator generates images
by parts based on their spatial coordinates as the condition. On the other
hand, the discriminator learns to justify realism across multiple assembled
patches by global coherence, local appearance, and edge-crossing continuity.
Despite the full images are never generated during training, we show that
COCO-GAN can produce \textbf{state-of-the-art-quality} full images during
inference. We further demonstrate a variety of novel applications enabled by
teaching the network to be aware of coordinates. First, we perform
extrapolation to the learned coordinate manifold and generate off-the-boundary
patches. Combining with the originally generated full image, COCO-GAN can
produce images that are larger than training samples, which we called
"beyond-boundary generation". We then showcase panorama generation within a
cylindrical coordinate system that inherently preserves horizontally cyclic
topology. On the computation side, COCO-GAN has a built-in divide-and-conquer
paradigm that reduces memory requisition during training and inference,
provides high-parallelism, and can generate parts of images on-demand.
