Hilbert fractal-structured liquid metal electrodes with isotropic stretchability and high conductivity

Stretchable electrodes with high conductivity and isotropic strain response are crucial for next-generation wearable electronics but remain challenging to achieve. In this work, a Hilbert fractal microchannel electrode filled with silver-coated copper doped eutectic gallium–indium liquid metal is presented. The fractal geometry provides uniform stress dispersion and balanced mechanical behavior in both principal directions, while the doped liquid metal improves interfacial adhesion and electrical stability. The electrodes exhibit an initial resistance of 0.59 Ω, with relative resistance changes of less than 30 % at 100 % strain in both the X and Y directions. The directional deviation is minimal, with percentage deviation values of 5.78 % at low strain and 1.38 % at high strain. They maintain stable performance after 100 loading cycles and across a temperature range of 20–60 °C, with a conductivity of approximately 7200 S/cm. Demonstrations in LED circuits and wrist-bending tests show nearly identical electromechanical responses under dynamic multidirectional deformation. These results address the persistent trade-off between stretchability and isotropy in flexible conductors and provide a scalable platform for applications in health monitoring, human–machine interfaces, and soft robotics.