A power-law tailed movement created by trajectory retracing

Tracing specific trajectories allows a walker to revisit previous locations. However, how such local memory-based rules influence large-scale movement patterns remains unclear. In this paper, we propose a single walker model that explores a two-dimensional lattice field and uses a limited directional memory that causes the walker to revisit previously encountered positions while sometimes maintaining long persistent movements. Simulation experiments reveal that our model exhibits a Lévy walk pattern through retracing based on recently experienced movement directions. Importantly, diffusiveness is likely to decrease if the memory length of walkers increases, suggesting that the walker can generate complex movement patterns using a limited directional memory.