Odell, G. M., Oster, G., Alberch, P. & Burnside, B. The mechanical basis of morphogenesis: I. Epithelial folding and invagination. Dev. Biol. 85, 446–462 (1981).


Google Scholar
 

Dawes-Hoang, R. E. et al. folded gastrulation, cell shape change and the control of myosin localization. Development 132, 4165–4178 (2005).


Google Scholar
 

Martin, A. C. & Goldstein, B. Apical constriction: themes and variations on a cellular mechanism driving morphogenesis. Development 141, 1987–1998 (2014).


Google Scholar
 

Tozluoglu, M. et al. Planar differential growth rates initiate precise fold positions in complex epithelia. Dev. Cell 51, 299–3124 (2019).


Google Scholar
 

Savin, T. et al. On the growth and form of the gut. Nature 476, 57–62 (2011).

ADS 

Google Scholar
 

Collinet, C. & Lecuit, T. Programmed and self-organized flow of information during morphogenesis. Nat. Rev. Mol. Cell Biol. 22, 245–265 (2021).


Google Scholar
 

Inoue, Y., Tateo, I. & Adachi, T. Epithelial tissue folding pattern in confined geometry. Biomech. Model. Mechanobiol. 19, 815–822 (2020).


Google Scholar
 

Münster, S. et al. Attachment of the blastoderm to the vitelline envelope affects gastrulation of insects. Nature 568, 395–399 (2019).

ADS 

Google Scholar
 

Sui, L. et al. Differential lateral and basal tension drive folding of Drosophila wing discs through two distinct mechanisms. Nat. Commun. 9, 4620 (2018).

ADS 

Google Scholar
 

Akula, S. K., Exposito-Alonso, D. & Walsh, C. A. Shaping the brain: the emergence of cortical structure and folding. Dev. Cell 58, 2836–2849 (2023).


Google Scholar
 

Nikolopoulou, E., Galea, G. L., Rolo, A., Greene, N. D. E. & Copp, A. J. Neural tube closure: cellular, molecular and biomechanical mechanisms. Development 144, 552–566 (2017).


Google Scholar
 

Schenk, M. et al. Origami folding: a structural engineering approach. Origami 5, 291–304 (2011).


Google Scholar
 

McShane, S. G. et al. Cellular basis of neuroepithelial bending during mouse spinal neural tube closure. Dev. Biol. 404, 113–124 (2015).


Google Scholar
 

Yue, S. A review of origami-based deployable structures in aerospace engineering. J. Phys. Conf. Ser. 2459, 012137 (2023).


Google Scholar
 

Andrejevic, J., Lee, L. M., Rubinstein, S. M. & Rycroft, C. H. A model for the fragmentation kinetics of crumpled thin sheets. Nat. Commun. 12, 1470 (2021).

ADS 

Google Scholar
 

Aharoni, H. & Sharon, E. Direct observation of the temporal and spatial dynamics during crumpling. Nat. Mater. 9, 993–997 (2010).


Google Scholar
 

Gottesman, O., Andrejevic, J., Rycroft, C. H. & Rubinstein, S. M. A state variable for crumpled thin sheets. Commun. Phys. 1, 70 (2018).


Google Scholar
 

Leal, F. C. B. & Gomes, M. A. F. Unfolding of crumpled thin sheets. Phys. Rev. E 106, 025002 (2022).

ADS 

Google Scholar
 

Davidovitch, B. & Démery, V. Rucks and folds: delamination from a flat rigid substrate under uniaxial compression. Eur. Phys. J. E 44, 11 (2021).


Google Scholar
 

Box, F. et al. Dynamics of wrinkling in ultrathin elastic sheets. Proc. Natl Acad. Sci. USA 116, 20875–20880 (2019).

ADS 
MathSciNet 

Google Scholar
 

Liu, S. et al. Conformability of flexible sheets on spherical surfaces. Sci. Adv. 9, 2709 (2023).


Google Scholar
 

Fouchard, J. et al. Curling of epithelial monolayers reveals coupling between active bending and tissue tension. Proc. Natl Acad. Sci. USA 117, 9377–9383 (2020).

ADS 

Google Scholar
 

Schmalholz, S. M. & Schmid, D. W. Folding in power-law viscous multi-layers. Phil. Trans. R. Soc. A 370, 1798–1826 (2012).

ADS 

Google Scholar
 

Peraza Hernandez, H. D., Edwin, A. & Lagoudas, D. Active Origami: Modeling, Designs, and Applications (Springer, 2019).

Mu, J. et al. Origami-inspired active graphene-based paper for programmable instant self-folding walking devices. Sci. Adv. 1, 1500533 (2015).

ADS 

Google Scholar
 

Sato, Y., Terashima, S. & Iwase, E. Origami-type flexible thermoelectric generator fabricated by self-folding. Micromachines https://doi.org/10.3390/mi14010218 (2023).

Leanza, S., Wu, S., Sun, X., Qi, H. J. & Zhao, R. R. Active materials for functional origami. Adv. Mater. 36, 2302066 (2024).


Google Scholar
 

Ge, Q., Dunn, C. K., Qi, H. J. & Dunn, M. L. Active origami by 4D printing. Smart Mater. Struct. 23, 094007 (2014).

ADS 

Google Scholar
 

Felton, S., Tolley, M., Demaine, E., Rus, D. & Wood, R. A method for building self-folding machines. Science 345, 644–646 (2014).

ADS 

Google Scholar
 

Liu, Y., Shaw, B., Dickey, M. D. & Genzer, J. Sequential self-folding of polymer sheets. Sci. Adv. 3, 1602417 (2017).

ADS 

Google Scholar
 

Randall, C. L., Gultepe, E. & Gracias, D. H. Self-folding devices and materials for biomedical applications. Trends Biotechnol. 30, 138–146 (2012).


Google Scholar
 

Novelino, L. S., Ze, Q., Wu, S., Paulino, G. H. & Zhao, R. Untethered control of functional origami microrobots with distributed actuation. Proc. Natl Acad. Sci. USA17, 24096–24101 (2020).

ADS 

Google Scholar
 

Zartman, J. J. & Shvartsman, S. Y. Unit operations of tissue development: epithelial folding. Annu. Rev. Chem. Biomol. Eng. 1, 231–246 (2010).


Google Scholar
 

Brannon, C. M. & Prakash, M. Cilia-driven epithelial folding and unfolding in an early diverging animal. Proc. Natl Acad. Sci. USA 122, 2517741122 (2025).


Google Scholar
 

Smith, C. L. et al. Novel cell types, neurosecretory cells, and body plan of the early-diverging metazoan trichoplax adhaerens. Curr. Biol. 24, 1565–1572 (2014).


Google Scholar
 

Bull, M.S., Prakash, V.N. & Prakash, M. Ciliary flocking and emergent instabilities enable collective agility in a non-neuromuscular animal. Preprint at https://arxiv.org/abs/2107.02934 (2021).

Davidescu, M. R., Romanczuk, P., Gregor, T. & Couzin, I. D. Growth produces coordination trade-offs in Trichoplax adhaerens, an animal lacking a central nervous system. Proc. Natl Acad. Sci. USA 120, 2206163120 (2023).


Google Scholar
 

Pieranski, P., Godinho, M.H. Collisions of monopoles, disclinations and dislocations. Eur. Phys. J. Spec. Top. https://doi.org/10.1140/epjs/s11734-024-01253-9 (2024).

Bull, M. S., Kroo, L. A. & Prakash, M. Excitable mechanics embodied in a walking cilium. Preprint at https://arxiv.org/abs/2107.02930 (2021).

Madhu, G.et al. in Advancements in Optical Methods, Digital Image Correlation & Mechanics of Biological Systems and Materials Vol. 2 (eds Hwang, C.-H., Shaw, G. A., Fujigaki, M., Kasza, K. & McGhee, A.) 83–88 (Springer, 2025).

Prakash, V. N., Bull, M. S. & Prakash, M. Motility-induced fracture reveals a ductile-to-brittle crossover in a simple animal’s epithelia. Nat. Phys. 17, 504–511 (2021).


Google Scholar
 

Chopin, J., Démery, V. & Davidovitch, B. Roadmap to the morphological instabilities of a stretched twisted ribbon. J. Elast. 119, 137–189 (2015).

MathSciNet 

Google Scholar
 

Leria, M.et al. Fast mechanosensitive and Ca2+-dependent reorientation of motile cilia basal bodies in the placozoan, Trichoplax. Curr Biol. https://doi.org/10.1016/j.cub.2026.04.054 (2026).

Bouffanais, R. in An Information-Theoretic Approach to Collective Behaviors 75–93 (Springer, 2016); https://doi.org/10.1007/978-981-287-751-2_5.

Vella, D., Boudaoud, A. & Adda-Bedia, M. Statics and inertial dynamics of a ruck in a rug. Phys. Rev. Lett. 103, 174301 (2009).

ADS 

Google Scholar
 

Dey, B.et al. Divergent evolutionary strategies pre-empt tissue collision in gastrulation. Nature 646, 637–646 (2025).

Vellutini, B.C.et al. Patterned invagination prevents mechanical instability during gastrulation. Nature 646, 627–636 (2025).

Shankar, S., Souslov, A., Bowick, M. J., Marchetti, M. C. & Vitelli, V. Topological active matter. Nat. Rev. Phys. 4, 380–398 (2022).


Google Scholar
 

Hamm, E., Roman, B. & Melo, F. Dynamics of developable cones under shear. Phys. Rev. E 70, 026607 (2004).

ADS 

Google Scholar
 

Gottesman, O., Efrati, E. & Rubinstein, S. M. Furrows in the wake of propagating d-cones. Nat. Commun. 6, 7232 (2015).

ADS 

Google Scholar
 

Witten, T. A. Stress focusing in elastic sheets. Rev. Mod. Phys. 79, 643–675 (2007).

ADS 
MathSciNet 

Google Scholar
 

Wong, R. H. C. & Chau, K. T. Crack coalescence in a rock-like material containing two cracks. Int. J. Rock Mech. Min. Sci. 35, 147–164 (1998).


Google Scholar
 

Dias, M. A., Dudte, L. H., Mahadevan, L. & Santangelo, C. D. Geometric mechanics of curved crease origami. Phys. Rev. Lett. 109, 114301 (2012).

ADS 

Google Scholar
 

Dias, M. A. & Audoly, B. A non-linear rod model for folded elastic strips. J. Mech. Phys. Solids 62, 57–80 (2014).

ADS 
MathSciNet 

Google Scholar
 

Nasti, G. et al. Patterning of perovskite-polymer films by wrinkling instabilities. Soft Matter 13, 1654–1659 (2017).

ADS 

Google Scholar
 

Brannon, C. M. & Prakash, M. Creases act as information bottlenecks in active elastic sheets. Dryad https://doi.org/10.5061/dryad.msbcc2gd0 (2026).