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Analysis of emergent patterns in crossing flows of pedestrians reveals an invariant of ‘stripe’ formation in human data
When two streams of pedestrians cross at an angle, striped patterns spontaneously emerge as a result of local pedestrian interactions. This clear case of self-organized pattern formation remains to be elucidated. In counterflows, with a crossing angle of 180°, alternating lanes of traffic are common...
Autores principales: | , , , , , |
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Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
Public Library of Science
2022
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Materias: | |
Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9216623/ https://www.ncbi.nlm.nih.gov/pubmed/35679329 http://dx.doi.org/10.1371/journal.pcbi.1010210 |
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author | Mullick, Pratik Fontaine, Sylvain Appert-Rolland, Cécile Olivier, Anne-Hélène Warren, William H. Pettré, Julien |
author_facet | Mullick, Pratik Fontaine, Sylvain Appert-Rolland, Cécile Olivier, Anne-Hélène Warren, William H. Pettré, Julien |
author_sort | Mullick, Pratik |
collection | PubMed |
description | When two streams of pedestrians cross at an angle, striped patterns spontaneously emerge as a result of local pedestrian interactions. This clear case of self-organized pattern formation remains to be elucidated. In counterflows, with a crossing angle of 180°, alternating lanes of traffic are commonly observed moving in opposite directions, whereas in crossing flows at an angle of 90°, diagonal stripes have been reported. Naka (1977) hypothesized that stripe orientation is perpendicular to the bisector of the crossing angle. However, studies of crossing flows at acute and obtuse angles remain underdeveloped. We tested the bisector hypothesis in experiments on small groups (18-19 participants each) crossing at seven angles (30° intervals), and analyzed the geometric properties of stripes. We present two novel computational methods for analyzing striped patterns in pedestrian data: (i) an edge-cutting algorithm, which detects the dynamic formation of stripes and allows us to measure local properties of individual stripes; and (ii) a pattern-matching technique, based on the Gabor function, which allows us to estimate global properties (orientation and wavelength) of the striped pattern at a time T. We find an invariant property: stripes in the two groups are parallel and perpendicular to the bisector at all crossing angles. In contrast, other properties depend on the crossing angle: stripe spacing (wavelength), stripe size (number of pedestrians per stripe), and crossing time all decrease as the crossing angle increases from 30° to 180°, whereas the number of stripes increases with crossing angle. We also observe that the width of individual stripes is dynamically squeezed as the two groups cross each other. The findings thus support the bisector hypothesis at a wide range of crossing angles, although the theoretical reasons for this invariant remain unclear. The present results provide empirical constraints on theoretical studies and computational models of crossing flows. |
format | Online Article Text |
id | pubmed-9216623 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2022 |
publisher | Public Library of Science |
record_format | MEDLINE/PubMed |
spelling | pubmed-92166232022-06-23 Analysis of emergent patterns in crossing flows of pedestrians reveals an invariant of ‘stripe’ formation in human data Mullick, Pratik Fontaine, Sylvain Appert-Rolland, Cécile Olivier, Anne-Hélène Warren, William H. Pettré, Julien PLoS Comput Biol Research Article When two streams of pedestrians cross at an angle, striped patterns spontaneously emerge as a result of local pedestrian interactions. This clear case of self-organized pattern formation remains to be elucidated. In counterflows, with a crossing angle of 180°, alternating lanes of traffic are commonly observed moving in opposite directions, whereas in crossing flows at an angle of 90°, diagonal stripes have been reported. Naka (1977) hypothesized that stripe orientation is perpendicular to the bisector of the crossing angle. However, studies of crossing flows at acute and obtuse angles remain underdeveloped. We tested the bisector hypothesis in experiments on small groups (18-19 participants each) crossing at seven angles (30° intervals), and analyzed the geometric properties of stripes. We present two novel computational methods for analyzing striped patterns in pedestrian data: (i) an edge-cutting algorithm, which detects the dynamic formation of stripes and allows us to measure local properties of individual stripes; and (ii) a pattern-matching technique, based on the Gabor function, which allows us to estimate global properties (orientation and wavelength) of the striped pattern at a time T. We find an invariant property: stripes in the two groups are parallel and perpendicular to the bisector at all crossing angles. In contrast, other properties depend on the crossing angle: stripe spacing (wavelength), stripe size (number of pedestrians per stripe), and crossing time all decrease as the crossing angle increases from 30° to 180°, whereas the number of stripes increases with crossing angle. We also observe that the width of individual stripes is dynamically squeezed as the two groups cross each other. The findings thus support the bisector hypothesis at a wide range of crossing angles, although the theoretical reasons for this invariant remain unclear. The present results provide empirical constraints on theoretical studies and computational models of crossing flows. Public Library of Science 2022-06-09 /pmc/articles/PMC9216623/ /pubmed/35679329 http://dx.doi.org/10.1371/journal.pcbi.1010210 Text en © 2022 Mullick et al https://creativecommons.org/licenses/by/4.0/This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0/) , which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. |
spellingShingle | Research Article Mullick, Pratik Fontaine, Sylvain Appert-Rolland, Cécile Olivier, Anne-Hélène Warren, William H. Pettré, Julien Analysis of emergent patterns in crossing flows of pedestrians reveals an invariant of ‘stripe’ formation in human data |
title | Analysis of emergent patterns in crossing flows of pedestrians reveals an invariant of ‘stripe’ formation in human data |
title_full | Analysis of emergent patterns in crossing flows of pedestrians reveals an invariant of ‘stripe’ formation in human data |
title_fullStr | Analysis of emergent patterns in crossing flows of pedestrians reveals an invariant of ‘stripe’ formation in human data |
title_full_unstemmed | Analysis of emergent patterns in crossing flows of pedestrians reveals an invariant of ‘stripe’ formation in human data |
title_short | Analysis of emergent patterns in crossing flows of pedestrians reveals an invariant of ‘stripe’ formation in human data |
title_sort | analysis of emergent patterns in crossing flows of pedestrians reveals an invariant of ‘stripe’ formation in human data |
topic | Research Article |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9216623/ https://www.ncbi.nlm.nih.gov/pubmed/35679329 http://dx.doi.org/10.1371/journal.pcbi.1010210 |
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