While living organisms have mastered the dynamic control of residual stresses within sheets to induce shape transformation and locomotion, man-made implementations are rudimentary. We present the first autonomously shape-shifting sheets made of a gel that shrinks and swells in response to the phase of an oscillatory chemical (Belousov-Zhabotinsky) reaction. Propagating reaction-diffusion fronts induce localized deformation of the gel. We show that these localized deformations prescribe a spatiotemporal pattern of Gaussian curvature, leading to time-periodic global shape changes. We present the computational tools and experimental protocols needed to control this system, principally the relationship between the Gaussian curvature and the reaction phase, and optical imprinting of the wave pattern. Together, our results demonstrate a route for developing fully autonomous soft machines mimicking some of the locomotive capabilities of living organisms.

中文翻译：

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自振荡膜：化学机械片显示自主周期性形状转换。

虽然生物体已经掌握了板料内部残余应力的动态控制，以诱导形状转变和运动，但人工实施是基本的。我们介绍了由凝胶制成的第一个自主变形的片，该片根据振荡化学反应（Belousov-Zhabotinsky）反应的阶段而收缩和膨胀。传播的反应扩散前沿引起凝胶的局部变形。我们表明，这些局部变形规定了高斯曲率的时空模式，从而导致时间周期的整体形状变化。我们介绍了控制该系统所需的计算工具和实验协议，主要是高斯曲率和反应相位之间的关系，以及波型的光学印迹。一起，