Multi-hierarchical movements in self-avoiding walks

Tomoko Sakiyama*, Yukio Pegio Gunji

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contribution


A self-avoiding walk (SAW) is a series of moves on a lattice that visit the same place only once. Several studies reported that repellent reactions of foragers to previously visited sites induced power-law tailed SAWs in animals. In this paper, we show that modelling the agent's multi-avoidance reactions to its trails enables it to show ballistic movements which result in heavy-tailed movements. There is no literature showing emergent ballistic movements in SAWs. While following SAWs, the agent in my model changed its reactions to marked patches (visited sites) by considering global trail patterns based on local trail patterns when the agent was surrounded by previously visited sites. As a result, we succeeded in producing ballistic walks by the agents which exhibited emergent power-law tailed movements.

Original languageEnglish
Title of host publicationInternational Conference of Numerical Analysis and Applied Mathematics, ICNAAM 2016
EditorsTheodore E. Simos, Theodore E. Simos, Charalambos Tsitouras
PublisherAmerican Institute of Physics Inc.
ISBN (Electronic)9780735415386
Publication statusPublished - 2017 Jul 21
EventInternational Conference of Numerical Analysis and Applied Mathematics 2016, ICNAAM 2016 - Rhodes, Greece
Duration: 2016 Sept 192016 Sept 25

Publication series

NameAIP Conference Proceedings
ISSN (Print)0094-243X
ISSN (Electronic)1551-7616


OtherInternational Conference of Numerical Analysis and Applied Mathematics 2016, ICNAAM 2016

ASJC Scopus subject areas

  • Physics and Astronomy(all)


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