  Quasi-periodic structures of quasicrystals yield novel effects in diverse
systems. However, there is little investigation on employing quasi-periodic
structures in the morphology control. Here, we show the use of quasi-periodic
surface structures in controlling the transition of liquid droplets. Although
surface structures seem random-like, we find that on these surfaces, droplets
spread to well-defined 5-fold symmetric shapes and the symmetry of droplet
shapes spontaneously restore during spreading, hitherto unreported in the
morphology control of droplets. To obtain physical insights into these symmetry
transitions, we conduct energy analysis and perform systematic experiments by
varying properties of both liquid droplet and patterned surface. The results
show the dominant factors in determining droplet shapes to be surface
topography and the self-similarity of the surface structure. Our findings
significantly advance the control capability of the droplet morphology. Such a
quasi-periodic patterning strategy can offer a new method to achieve complex
patterns.
