Cumulative culture enables humans to preserve, reuse, and extend knowledge and skills across experiences and generations. Inspired by this principle, we introduce \textit{SimSkill}, a self-evolving agent built around the Simulation of Urban MObility (SUMO) traffic simulator. SimSkill continually identifies capability gaps, generates and solves environment-grounded tasks, verifies solutions through an action--critic loop, and consolidates experience into episodic, procedural, and semantic memory. Through autonomous exploration, it builds a library of reusable skills and knowledge spanning major stages of the traffic-simulation workflow. We evaluate SimSkill on two held-out benchmarks across three backbone LLMs, with each result independently verified. It improves verified success by up to 25 percentage points, and ablations show complementary contributions from procedural and semantic memory. Its benefits remain backbone- and budget-dependent, as memory does not improve every model or uniformly reduce inference cost. More broadly, SimSkill illustrates a natural-language-centered design paradigm for LLM-based agent systems. Its high-level control logic, operating principles, and accumulated knowledge are expressed in natural language, while an LLM integrates them with executable tools and code to realize precise and reproducible execution. All code and experimental data are publicly available at https://github.com/qiliuchn/SimSkill-V1.

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