We introduce LivingWorld, an interactive framework for generating 4D worlds with environmental dynamics from a single image. While recent advances in 3D scene generation enable large-scale environment creation, most approaches focus primarily on reconstructing static geometry, leaving scene-scale environmental dynamics such as clouds, water, or smoke largely unexplored. Modeling such dynamics is challenging because motion must remain coherent across an expanding scene while supporting low-latency user feedback. LivingWorld addresses this challenge by progressively constructing a globally coherent motion field as the scene expands. To maintain global consistency during expansion, we introduce a geometry-aware alignment module that resolves directional and scale ambiguities across views. We further represent motion using a compact hash-based motion field, enabling efficient querying and stable propagation of dynamics throughout the scene. This representation also supports bidirectional motion propagation during rendering, producing long and temporally coherent 4D sequences without relying on expensive video-based refinement. On a single RTX 5090 GPU, generating each new scene expansion step requires 9 seconds, followed by 3 seconds for motion alignment and motion field updates, enabling interactive 4D world generation with globally coherent environmental dynamics. Video demonstrations are available at cvsp-lab.github.io/LivingWorld.