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Journal of Interdisciplinary Mathematics cover
Hybrid ·Peer-reviewed·ISSN (Online): 2169-012X·ISSN (Print): 0972-0502

Monthly Journal: Publishes the methodological and theoretical role of mathematics and mathematical applications underpinning scientific research.

Issues up to 2022 co-published with and available at:Taylor & Francis Online
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Open Access Research Article

Planning a dynamical movement of patterns based on groups relations

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pp. 1505–1516Vol. 28Issue 4June 2025DOI: 10.47974/JIM-2069XML
Received:
09 Apr 2024
Published Online:
21 May 2025
Article type:
Research Article
Language:
EN
Article no.:
JIM-2069
Pages:
1505–1516

Abstract

Dynamical movement between different stages in a given product can be challenging. In this manuscript, we will show how groups relations indicate if exists dynamical movement between different stages in a given product defined by planner patterns, and what is the respective mechanism that defines this dynamical tiling. Our construction can be applied to folding tables (reduction and expansions), lightning systems (exposure, and hiding), and more.

Keywords

Subject Classifications

20A0570E1705B99

References

[1] B. Berman, “3-D Printing: The New Industrial Revolution,” Business Horizons, vol. 55, no. 2, pp. 155–162 (2012).
[2] K. Neuburg, S. Quadflieg, and S. Nestler, “Will Artificial Intelligence Make Designers Obsolete?” in Proc. First Conf. Designing with Artificial Intelligence, München: appliedAI, pp. 80–85 (2021).
[3] K. Warisaya, J. Sato, and T. Tachi, “Freeform Auxetic Mechanisms Based on Corner-Connected Tiles,” Journal of the International Association for Shell and Spatial Structures, vol. 63, no. 4, pp. 263–271 (2022).
[4] J. Hervé, “The Lie Group of Rigid Body Displacements, a Fundamental Tool for Mechanism Design,” Mechanism and Machine Theory, vol. 34, no. 5, pp. 719–730 (1999). [Online]. Available: https://www.sciencedirect.com/science/article/pii/S0094114X98000512.
[5] R. Watada, M. Ohsaki, and Y. Kanno, “Group Theoretic Approach to Large-Deformation Property of Three-Dimensional Bar-Hinge Mechanism,” Japan Journal of Industrial and Applied Mathematics, vol. 36, pp. 177–208 (2019).
[6] A. Derouet-Jourdan, S. Kaji, and Y. Mizoguchi, “A Linear Algorithm for Brick Wang Tiling,” Japan Journal of Industrial and Applied Mathematics, vol. 36, pp. 749–761 (2019).
[7] “The Fletcher Capstan Table,” March (2023). [Online]. Available: https://www.youtube.com/watch?v=hsmTPBToih4. [Accessed: Mar. 2023].
[8] “Expanding Table,” May (2020). [Online]. Available: https://www.youtube.com/watch?v=L5w16WtRQ1I. [Accessed: May 2020].
[9] K. Kshirsagar, “Hex-Flex,” Bridges Aalto 2022 Art Exhibition Catalog. [Online]. Available: http://gallery.bridgesmathart.org/exhibitions/2022-bridges-conference/kkshir.
[10] P. Amsellem and S. Gul, “Dynamical Tilings in Industrial Design,” in Proc. Bridges 2023: Mathematics, Art, Music, Architecture, Culture, J. Holdener, E. Torrence, C. Fong, and K. Seaton, Eds. Phoenix, Arizona: Tessellations Publishing, pp. 413–416 (2023). [Online]. Available: http://archive.bridgesmathart.org/2023/bridges2023-413.html.
[11] J. H. Conway, H. Burgiel, and C. Goodman-Strauss, The Symmetries of Things. Taylor and Francis Group: CRC Press (2016).
[12] “Dynamical Tiling - 632,” Sep. (2013). [Online]. Available: https://www.youtube.com/watch?v=rhO6J8cZK20. [Accessed: Sep. 2013].

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