The Complexity of Folding Self-Folding Origami
Why is it difficult to refold a previously folded sheet of paper? We show that even crease patterns with only one designed folding motion inevitably contain an exponential number of “distractor” folding branches accessible from a bifurcation at the flat state. Consequently, refolding a sheet require...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
American Physical Society
2017-12-01
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| Series: | Physical Review X |
| Online Access: | http://doi.org/10.1103/PhysRevX.7.041070 |
| _version_ | 1829495768485986304 |
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| author | Menachem Stern Matthew B. Pinson Arvind Murugan |
| author_facet | Menachem Stern Matthew B. Pinson Arvind Murugan |
| author_sort | Menachem Stern |
| collection | DOAJ |
| description | Why is it difficult to refold a previously folded sheet of paper? We show that even crease patterns with only one designed folding motion inevitably contain an exponential number of “distractor” folding branches accessible from a bifurcation at the flat state. Consequently, refolding a sheet requires finding the ground state in a glassy energy landscape with an exponential number of other attractors of higher energy, much like in models of protein folding (Levinthal’s paradox) and other NP-hard satisfiability (SAT) problems. As in these problems, we find that refolding a sheet requires actuation at multiple carefully chosen creases. We show that seeding successful folding in this way can be understood in terms of subpatterns that fold when cut out (“folding islands”). Besides providing guidelines for the placement of active hinges in origami applications, our results point to fundamental limits on the programmability of energy landscapes in sheets. |
| first_indexed | 2024-12-16T07:16:34Z |
| format | Article |
| id | doaj.art-e859c682505e4e78b7975d70e9864acb |
| institution | Directory Open Access Journal |
| issn | 2160-3308 |
| language | English |
| last_indexed | 2024-12-16T07:16:34Z |
| publishDate | 2017-12-01 |
| publisher | American Physical Society |
| record_format | Article |
| series | Physical Review X |
| spelling | doaj.art-e859c682505e4e78b7975d70e9864acb2022-12-21T22:39:45ZengAmerican Physical SocietyPhysical Review X2160-33082017-12-017404107010.1103/PhysRevX.7.041070The Complexity of Folding Self-Folding OrigamiMenachem SternMatthew B. PinsonArvind MuruganWhy is it difficult to refold a previously folded sheet of paper? We show that even crease patterns with only one designed folding motion inevitably contain an exponential number of “distractor” folding branches accessible from a bifurcation at the flat state. Consequently, refolding a sheet requires finding the ground state in a glassy energy landscape with an exponential number of other attractors of higher energy, much like in models of protein folding (Levinthal’s paradox) and other NP-hard satisfiability (SAT) problems. As in these problems, we find that refolding a sheet requires actuation at multiple carefully chosen creases. We show that seeding successful folding in this way can be understood in terms of subpatterns that fold when cut out (“folding islands”). Besides providing guidelines for the placement of active hinges in origami applications, our results point to fundamental limits on the programmability of energy landscapes in sheets.http://doi.org/10.1103/PhysRevX.7.041070 |
| spellingShingle | Menachem Stern Matthew B. Pinson Arvind Murugan The Complexity of Folding Self-Folding Origami Physical Review X |
| title | The Complexity of Folding Self-Folding Origami |
| title_full | The Complexity of Folding Self-Folding Origami |
| title_fullStr | The Complexity of Folding Self-Folding Origami |
| title_full_unstemmed | The Complexity of Folding Self-Folding Origami |
| title_short | The Complexity of Folding Self-Folding Origami |
| title_sort | complexity of folding self folding origami |
| url | http://doi.org/10.1103/PhysRevX.7.041070 |
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