Classical cellular automata are simple algorithms that result in a suprisingly rich range of complex phenomena. On our dual-species Rydberg array we have now implemented their quantum version: quantum cellular automata. With simple global driving we achieve a whole myriad of quantum protocols ranging from growing entangled states (GHZ and cluster states) to studying quasiparticle dynamics. The versatility and scalability of this approach present compelling opportunities for the development of quantum information systems, as well as new perspectives on quantum many-body dynamics. Check out our work here: Quantum Cellular Automata on a Dual-Species Rydberg Processor