Fig. 1

The origin of self-oscillation in natural and in artificial light-fuelled systems. a, b Photographs of a leaf self-oscillating under a breeze. Inset of b shows time-dependent displacement of the centre of mass of the leaf, indicating periodic movement with well-defined frequency. Scale bar is 5 cm. A free-standing LCN actuator (c) bends slightly upon low-intensity irradiation (50 mW cm⁻², d) and more pronouncedly when the intensity is increased (200 mW cm⁻², e). f–h Schematic drawings showing the qualitative dependence between absorbed energy E, deformation D, effective light-absorbing area A, and equilibrium position upon illumination. i Harmonic oscillator (solid line, numerical solution to equation, \(\ddot x + \omega _{\mathrm{o}}^2x = 0\)) and an oscillator experiencing damping (dashed line, numerical solution to equation, \(\ddot x + \varsigma \dot x + \omega _{\mathrm{o}}^2x = 0\)), where ω₀ = 2π, \(\dot x\left( 0 \right) = 0,x\left( 0 \right) = 1\), \(\varsigma = 0.1\). Self-oscillation induced by j a minor time delay σ and k a large σ. Numerical solutions to equation \(\ddot x - \left( {\sigma \omega _{\mathrm{o}}^2 - \varsigma - \eta x^2} \right)\dot x + \omega _{\mathrm{o}}^2x = 0\), where \(\varsigma = 0.1,\omega _0 = 2{\mathrm{\pi }}\), \(\dot x\left( 0 \right) = 1,x\left( 0 \right) = 0\), and \(\sigma \omega _{\mathrm{o}}^2 = 1,\eta = 3\) in j and \(\sigma \omega _{\mathrm{o}}^2 = 20,\eta = 60\) in k