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The rapid progress of Large Language Models has advanced agentic systems in decision-making, coordination, and task execution. Yet, existing agentic system generation frameworks lack full autonomy, missing from-scratch agent generation, self-optimizing functionality, and collaboration, limiting adaptability and automation. We propose SwarmAgentic, a framework for fully automated agentic system generation, extending Particle Swarm Optimization (PSO) into a language-driven search space for structure-level optimization. SwarmAgentic instantiates agents from scratch and jointly optimizes agent functionality and collaboration as interdependent components. We evaluate our method on six real-world, open-ended, and exploratory tasks involving high-level planning, system-level coordination, and creative reasoning. Given only a task description and an objective function, SwarmAgentic outperforms all baselines, achieving a +261.8% relative improvement over ADAS on the TravelPlanner benchmark, highlighting the effectiveness of full automation in structurally unconstrained tasks. This framework marks a significant step toward scalable and autonomous agentic system design, bridging swarm intelligence with fully automated system multi-agent generation.