Simulating activity-pressure formation and adaptive redistribution in a historic district: a physarum-inspired multi-agent approach

Historic districts face increasing challenges due to the coexistence of intensive tourism, residents' everyday life, and sensitive ecological environments within constrained urban spaces. To address this issue, using the Shichahai historic district in Beijing as a case study, this study develops a Physarum-inspired multi-agent simulation framework to examine activity-pressure patterns under different temporal and behavioral scenarios. Multi-source spatial data were translated into GAMA model inputs representing movement constraints, agent origins, temporal attraction fields, and redistribution targets. Resident, tourist, mixed-activity, and spatial attraction redistribution scenarios were constructed and repeatedly simulated to evaluate spatial coverage, path concentration, mean visit intensity, resident-tourist overlap, activity-pressure coupling, and model stability. The results show that the tourist scenario produced a more concentrated path, with active units ranging from 9,056 to 9,267 across the four observation dates, compared with approximately 10,639 -10,660 in the resident scenario and 10,721 -10,766 in the mixed scenario. The mixed scenario showed the highest overall mean visit intensity, with a mean-of-means visit value of 228.80, followed by the tourist scenario at 217.09 and the resident scenario at 212.82. Resident-tourist overlap remained low at the district scale, with a mean overlap index of approximately 0.023, while localized maximum values reached 0.958 -0.997, indicating that the co-concentration of simulated resident- and tourist-related movement was limited to specific corridors and nodes. Under the spatial attraction redistribution scenario, path concentration decreased, with HHI declining from approximately 5.45 -5.56 × 10 -4 to 4.19 × 10 -4 and the high-density visit share decreasing from 2.45% -2.76% to 0.95%. These findings indicate that adjusting high-density attraction clusters can reshape simulated path concentration and support a balanced distribution of activity pressure without changing the physical structure of the historic district. The proposed framework provides a dynamic modeling approach for identifying localized pressure concentration and supporting low-intervention environmental adaptive regulation in high-density historic districts.