A Short Memory Can Induce an Optimal Lévy Walk

In this paper, we investigate a possibility of the emergence of a Lévy walk using a single walker having a short memory. In our model, the walker recalls the past movement direction and compares it with the current direction. Based on the consistency or the inconsistency between these two information, the walker modifies the current directional rule. The walker in our model tends to move in a certain direction like a self-avoiding walk. For the walker, the coordination of the current rule implies that it can reconsider the directional rule. As a result, we found that the walker produced a power-law tailed movement called a Lévy walk which μ was close to an optimum (2.00). More importantly, the walker could not produce that characteristic movement if it could access not to a short-term memory but to a long-term memory. This finding suggests that the walker does not need any long-term memories to achieve an optimal walk like a Lévy walk.