Current Dynamic Texture Synthesis (DyTS) models in the literature can synthesize realistic videos. However, these methods require a slow iterative optimization process to synthesize a single fixed-size short video, and they do not offer any post-training control over the synthesis process. We propose Dynamic Neural Cellular Automata (DyNCA), a framework for real-time and controllable dynamic texture synthesis. Our method is built upon the recently introduced NCA models, and can synthesize infinitely-long and arbitrary-size realistic texture videos in real-time. We quantitatively and qualitatively evaluate our model and show that our synthesized videos appear more realistic than the existing results. We improve the SOTA DyTS performance by $2\sim 4$ orders of magnitude. Moreover, our model offers several real-time and interactive video controls including motion speed, motion direction, and an editing brush tool.