Weber-Fechner relation and Lévy-like searching stemmed from ambiguous experiences

T. Sakiyama*, Y. P. Gunji

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)


Abstract Here, we show that an optimized Lévy-like walk (μ≈2.00) and the Weber-Fechner law can be achieved in our new multi-agent based model that depends on step lengths. Weber-Fechner equation is strongly related to power-law. This equation is sometimes used in order to obtain power-law tailed distributions in observational levels. However, no study has reported how these two popular equations were achieved in micro or mechanistic levels. We propose a new random walk algorithm based on a re-valued algorithm, in which an agent has limited memory capacity, i.e., an agent has a memory of only four recent random numbers (limitation number). Using these random numbers, the agent alters the directional heuristic if the agent experiences moving directional biases. In this paper, the initial limitation number varies depending on the interaction among agents. Thus, agents change their limitation number and produce time delay in respect to rule change events. We show that slope values are variable compared with isolate foraging even though both indicate power-law tailed walks derived from Weber-Fechner equation.

Original languageEnglish
Article number16269
Pages (from-to)161-168
Number of pages8
JournalPhysica A: Statistical Mechanics and its Applications
Publication statusPublished - 2015 Jul 18


  • Power-law
  • Random walk
  • Weber-Fechner's law

ASJC Scopus subject areas

  • Statistics and Probability
  • Condensed Matter Physics


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