Hu, X. et al. Magnetic soft micromachines made of linked microactuator networks. Sci. Adv. 7, eabe8436 (2021).
Smart, C. L. et al. Magnetically programmed diffractive robotics. Science 386, 1031–1037 (2024).
Liu, Q. et al. Electronically configurable microscopic metasheet robots. Nat. Mater. 24, 109–115 (2024).
McMullen, A., Muñoz Basagoiti, M., Zeravcic, Z. & Brujic, J. Self-assembly of emulsion droplets through programmable folding. Nature 610, 502–506 (2022).
Melio, J., Henkes, S. E. & Kraft, D. J. Soft and stiff normal modes in floppy colloidal square lattices. Phys. Rev. Lett. 132, 078202 (2024).
Aubret, A., Martinet, Q. & Palacci, J. Metamachines of pluripotent colloids. Nat. Commun. 12, 6398 (2021).
Rinaldin, M., Verweij, R. W., Chakraborty, I. & Kraft, D. J. Colloid supported lipid bilayers for self-assembly. Soft Matter 15, 1345–1360 (2019).
van der Meulen, S. A. J. & Leunissen, M. E. Solid colloids with surface-mobile DNA linkers. J. Am. Chem. Soc. 135, 15129–15134 (2013).
Chakraborty, I., Meester, V., van der Wel, C. & Kraft, D. J. Colloidal joints with designed motion range and tunable joint flexibility. Nanoscale 9, 7814–7821 (2017).
Lubensky, T. C., Kane, C. L., Mao, X., Souslov, A. & Sun, K. Phonons and elasticity in critically coordinated lattices. Rep. Prog. Phys. 78, 073901 (2015).
Mullin, T., Deschanel, S., Bertoldi, K. & Boyce, M. C. Pattern transformation triggered by deformation. Phys. Rev. Lett. 99, 084301 (2007).
Grima, J. N. & Evans, K. E. Auxetic behavior from rotating squares. J. Mater. Sci. Lett. 19, 1563–1565 (2000).
Bertoldi, K., Vitelli, V., Christensen, J. & Van Hecke, M. Flexible mechanical metamaterials. Nat. Rev. Mater. 2, 17066 (2017).
Kadic, M., Milton, G. W., van Hecke, M. & Wegener, M. 3D metamaterials. Nat. Rev. Phys. 1, 198–210 (2019).
Resch, R. D. Geometrical device having articulated relatively movable sections. U.S. patent 3,201,894 (1963).
Guo, X., Guzmán, M., Carpentier, D., Bartolo, D. & Coulais, C. Non-orientable order and non-commutative response in frustrated metamaterials. Nature 618, 506–512 (2023).
Suzuki, Y. et al. Self-assembly of coherently dynamic, auxetic, two-dimensional protein crystals. Nature 533, 369–373 (2016).
Li, Y. et al. Ultrastrong colloidal crystal metamaterials engineered with DNA. Sci. Adv. 9, eadj8103 (2023).
Li, R., Chen, H. & Choi, J. H. Auxetic two-dimensional nanostructures from DNA. Angew. Chem. 60, 7165–7173 (2021).
Wang, Y. et al. Self-assembly of nanocrystal checkerboard patterns via non-specific interactions. Nat. Commun. 15, 3913 (2024).
Mao, X., Chen, Q. & Granick, S. Entropy favours open colloidal lattices. Nat. Mater. 12, 217–222 (2013).
Chen, Q., Bae, S. C. & Granick, S. Directed self-assembly of a colloidal kagome lattice. Nature 469, 381–384 (2011).
Zhang, Y. et al. One-step nanoscale assembly of complex structures via harnessing of an elastic instability. Nano Lett. 8, 1192–1196 (2008).
Dudek, K. K. et al. Micro-scale graded mechanical metamaterials exhibiting versatile Poisson’s ratio. Compos. Struct. 319, 117151 (2023).
Zhang, M. et al. Hydrogel muscles powering reconfigurable micro-metastructures with wide-spectrum programmability. Nat. Mater. 22, 1243–1252 (2023).
Xia, X. et al. Electrochemically reconfigurable architected materials. Nature 573, 205–213 (2019).
Frenzel, T., Kadic, M. & Wegener, M. Three-dimensional mechanical metamaterials with a twist. Science 358, 1072–1074 (2017).
Bückmann, T. et al. Tailored 3D mechanical metamaterials made by dip-in direct-laser-writing optical lithography. Adv. Mater. 24, 2710–2714 (2012).
Dorsey, K. J. et al. Atomic layer deposition for membranes, metamaterials, and mechanisms. Adv. Mater. 31, 1901944 (2019).
Barrat, J. L. et al. Soft matter roadmap. J. Phys. Mater. 7, 012501 (2023).
Dudek, K. K., Kadic, M., Coulais, C. & Bertoldi, K. Shape-morphing metamaterials. Nat. Rev. Mater. 10, 783–798 (2025).
Bishop, K. J. M., Biswal, S. L. & Bharti, B. Active colloids as models, materials, and machines. Annu. Rev. Chem. Biomol. Eng. 14, 1–30 (2023).
Liu, A. T. et al. Colloidal robotics. Nat. Mater. 22, 1453–1462 (2023).
Shelke, Y. et al. Flexible colloidal molecules with directional bonds and controlled flexibility. ACS Nano 17, 12234–12246 (2023).
Maxwell, J. C. L. On the calculation of the equilibrium and stiffness of frames. Lond. Edinb. Dublin Philos. Mag. J. Sci. 27, 294–299 (1864).
Sun, K., Souslov, A., Mao, X. & Lubensky, T. C. Surface phonons, elastic response, and conformal invariance in twisted kagome lattices. Proc. Natl Acad. Sci. USA 109, 12369–12374 (2012).
Shelke, Y., Pearce, D. J. G. & Kraft, D. J. Self-assembly pathways towards floppy colloidal square lattices. Nat. Commun. 17, 1040 (2025).
Mannattil, M., Schwarz, J. M. & Santangelo, C. D. Thermal fluctuations of singular bar-joint mechanisms. Phys. Rev. Lett. 128, 208005 (2022).
Broedersz, C. P. & Mackintosh, F. C. Modeling semiflexible polymer networks. Rev. Mod. Phys. 86, 995 (2014).
Dennison, M., Sheinman, M., Storm, C. & Mackintosh, F. C. Fluctuation-stabilized marginal networks and anomalous entropic elasticity. Phys. Rev. Lett. 111, 095503 (2013).
Stöber, W., Fink, A. & Bohn, E. Controlled growth of monodisperse silica spheres in the micron size range. J. Colloid Interface Sci. 26, 62–69 (1968).
Verweij, R. W., Melio, J., Chakraborty, I. & Kraft, D. J. Brownian motion of flexibly linked colloidal rings. Phys. Rev. E 107, 034602 (2023).
Barkley, S. et al. Holographic microscopy with Python and HoloPy. Comput. Sci. Eng. 22, 72–82 (2020).
Henkes, S., Brito, C. & Dauchot, O. Extracting vibrational modes from fluctuations: a pedagogical discussion. Soft Matter 8, 6092–6109 (2012).
Melio, J., van Hecke, M., Henkes, S. E. & Kraft, D. J. Colloidal pivots enable Brownian mechanical metamaterials. Datasets. Zenodo https://doi.org/10.5281/zenodo.14886689 (2026).

