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Microorganisms move in challenging environments by periodic changes in body shape. By contrast, current artificial microrobots cannot actively deform, exhibiting at best passive bending under external fields. Here, by taking advantage of the wireless, scalable and spatiotemporally selective capabilities that light allows, we show that soft microrobots consisting of photoactive liquid-crystal elastomers can be driven by structured monochromatic light to perform sophisticated biomimetic motions. We realized continuum yet selectively addressable artificial microswimmers that generate travelling-wave motions to self-propel without external forces or torques, as well as microrobots capable of versatile locomotion behaviours on demand. Both theoretical predictions and experimental results confirm that multiple gaits, mimicking either symplectic or antiplectic metachrony of ciliate protozoa, can be achieved with single microrobots. The principle of using structured light can be extended to other applications that require microscale actuation with sophisticated spatiotemporal coordination for advanced microrobotic technologies. 3Mobile micro-scale robots are envisioned to navigate within the human body to perform minimally invasive diagnostic or therapeutic tasks 1,2 . Biological microorganisms represent the natural inspiration for this vision. For instance, microorganisms successfully swim and move through a variety of fluids and tissues.Locomotion in this regime, where viscous forces dominate over inertia (low Reynolds number), is only possible through non-reciprocal motions demanding spatiotemporal coordination of multiple actuators 3 . A variety of biological propulsion mechanisms at different scales, from the peristalsis of annelids (Fig. 1a) to the metachrony of ciliates (Fig. 1b), are based on the common principle of travelling waves (Fig. 1c). These emerge from the distributed and self-coordinated action of many independent molecular motors 4,5 .Implementing travelling wave propulsion in an artificial device would require many discrete actuators, each individually addressed and powered in a coordinated fashion (Fig. 1d). The integration of actuators into microrobots that are mobile poses additional hurdles, since power and control need to be distributed without affecting the microrobots' mobility. Existing microscale actuators generally rely on applying external magnetic 6-10 , electric 11 , or optical 12,13 fields globally over the entire workspace. However, these approaches do not permit the spatial selectivity required to independently address individual actuators within a micro-device. Nevertheless, complex non-reciprocal motion patterns have been achieved by carefully engineering the response of different regions in a device to a spatially uniform external field 13,14 .The drawback is that this complicates the fabrication process, inhibits down-scaling and constrains the device to a single predefined behaviour. These challenges mean that most artificial microrobots actually have no actuators. Rather...

What began as a prediction about electron diffusion has spawned a rich variety of theories and experiments on the nature of the metal–insulator transition and the behavior of waves—from electromagnetic to seismic—in complex materials.

A random walk is a stochastic process in which particles or waves travel along random trajectories. The first application of a random walk was in the description of particle motion in a fluid (brownian motion); now it is a central concept in statistical physics, describing transport phenomena such as heat, sound and light diffusion. Lévy flights are a particular class of generalized random walk in which the step lengths during the walk are described by a 'heavy-tailed' probability distribution. They can describe all stochastic processes that are scale invariant. Lévy flights have accordingly turned out to be applicable to a diverse range of fields, describing animal foraging patterns, the distribution of human travel and even some aspects of earthquake behaviour. Transport based on Lévy flights has been extensively studied numerically, but experimental work has been limited and, to date, it has not seemed possible to observe and study Lévy transport in actual materials. For example, experimental work on heat, sound, and light diffusion is generally limited to normal, brownian, diffusion. Here we show that it is possible to engineer an optical material in which light waves perform a Lévy flight. The key parameters that determine the transport behaviour can be easily tuned, making this an ideal experimental system in which to study Lévy flights in a controlled way. The development of a material in which the diffusive transport of light is governed by Lévy statistics might even permit the development of new optical functionalities that go beyond normal light diffusion.