Despite increasingly realistic image quality, recent 3D image generative models often operate on 3D volumes of fixed extent with limited camera motions. We investigate the task of unconditionally synthesizing unbounded nature scenes, enabling arbitrarily large camera motion while maintaining a persistent 3D world model. Our scene representation consists of an extendable, planar scene layout grid, which can be rendered from arbitrary camera poses via a 3D decoder and volume rendering, and a panoramic skydome. Based on this representation, we learn a generative world model solely from single-view internet photos. Our method enables simulating long flights through 3D landscapes, while maintaining global scene consistency---for instance, returning to the starting point yields the same view of the scene. Our approach enables scene extrapolation beyond the fixed bounds of current 3D generative models, while also supporting a persistent, camera-independent world representation that stands in contrast to auto-regressive 3D prediction models. Our project page: https://chail.github.io/persistent-nature/.