The complexity of flat origami
WebHierarchical self-assembly of nanostructures with addressable complexity has been a promising route for realizing novel functional materials. Traditionally, the fabrication of such structures on a large scale has been achievable using top-down methods but with the cost of complexity of the fabrication equipment versus resolution and limitation mainly to 2D … WebApr 1, 2024 · A recent result Akitaya et al. (2024), further pointed out that it is weakly NP-hard to determine whether a degree-4 rigid origami (all the inner vertices are degree-4) can be folded flat (using ...
The complexity of flat origami
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WebDec 22, 2024 · B. Gin-ge Chen and C. D. Santangelo, Branches of Triangulated Origami near the Flat State, and , Branches of Triangulated Origami near the Flat State, arXiv:1706.03869. Y. V. Fyodorov, Complexity of Random Energy Landscapes, Glass Transition, and Absolute Value of the Spectral Determinant of Random Matrices, Phys. Rev. Lett. 92, 240601 (2004). WebCiteSeerX - Document Details (Isaac Councill, Lee Giles, Pradeep Teregowda): We study a basic problem in mathematical origami: determine if a given crease pattern can be folded to a flat origami. We show that assigning mountain and valley folds is NP-complete. We also show that determining a suitable overlap order for flaps is NP-complete, even assuming a …
WebJan 11, 2024 · This paper presents a preliminary quantitative model to analyze the complexity or difficulty of folding origami structures from flat membranes. Extensive … WebCiteSeerX - Document Details (Isaac Councill, Lee Giles, Pradeep Teregowda): Origami is the art of folding pieces of paper into works of sculpture without the aid of scissors or glue. Modern advancements in the complexity of origami (e.g., the work of Montroll and Maekawa) reveal a rich geometric structure governing the possibilities of paperfolding.
WebThis problem generalizes the classic theory of single-vertex flat origami with prescribed mountain-valley assignment, which corresponds to the case of a cycle graph. We characterize such flat-foldable plane graphs by two obviously necessary but also sufficient conditions, proving a conjecture made in 2001: the angles at each vertex should sum ... Web- Shown the act of folding self-folding origami to be a glassy (NP-complexity) problem. - Explored the design of self-folding origami systems with soft folding modes at any energy scale.
WebMar 24, 2024 · Flat Origami. An origami configuration that can be pressed to a plane figure without crumpling it or adding new creases. Kawasaki's Theorem, Maekawa's Theorem, …
WebApr 1, 2024 · A skilled Origami folder can create sophisticated three-dimensional figures from a simple square of paper. Regardless of its complexity, a folded figure can be transformed into its original form ... thunderbrew potion recipeWebFeb 16, 2024 · Complex designs, on the other hand, can take hours to complete. Some folders prefer almost cartoonlike renderings of their subjects, utilizing simple folding … thunderbrew hogwarts legacyWebBern, M., and Hayes, B. 1996. The complexity of flat origami. In Proceedings of the seventh annual ACM-SIAM symposium on Discrete algorithms, Society for Industrial and Applied Mathematics, Philadelphia, PA, USA, SODA '96, 175--183. Google Scholar Digital Library; Lang, R. J. 2012. Origami Design Secrets: Mathematical Methods for an Ancient Art. thunderbrew potion hogwartsWebHierarchical self-assembly of nanostructures with addressable complexity has been a promising route for realizing novel functional materials. Traditionally, the fabrication of … thunderbrew quest wow classicWebThe discipline of origami or paper folding has received a considerable amount of mathematical study. Fields of interest include a given paper model's flat-foldability … thunderbrew stoutWebJan 25, 2016 · The ability to create complex origami structures depends on folding thin sheets along creases, a natural consequence of the large-scale separation between the … thunderbrew\\u0027s boot flaskWebA Method for Designing Crease Patterns for Flat-Foldable Origami ... EN English Deutsch Français Español Português Italiano Român Nederlands Latina Dansk Svenska Norsk Magyar Bahasa Indonesia Türkçe Suomi Latvian … thunderbrew recipe hogwarts