Many plants autonomously change morphology and function in response to environmental stimuli or sequences of stimuli. In contrast with the electronically-integrated sensors, actuators, and microprocessors in traditional mechatronic systems, natural systems embody these sensing, actuation, and control functions within their compositional and structural features. Inspired by nature, we embody logic in autonomous systems to enable them to respond to multiple stimuli. Using 3D printable fibrous composites, we fabricate structures with geometries near bifurcation points associated with a transition between bistability and monostability. When suitable stimuli are present, the materials swell anisotropically. This forces a key geometric parameter to pass through a bifurcation, triggering rapid and large-amplitude self-actuation. The actuation time can be programmed by varying structural parameters (from 0.6 to 108 s for millimeter-scale structures). We demonstrate this bioinspired control strategy with examples that respond to their environment according to their embodied logic, without electronics, external control, or tethering.