Topology-defined computation in knitted textiles

Abstract: Mechanical computation, in which logic functions are realized through deformation rather than electronics, has been demonstrated in systems such as origami, kirigami, and mechanical metamaterials. In these systems, logic states and functions are typically determined by geometry and material properties, making it sensitive to deformation and imperfections. Here we introduce a mechanical computing architecture in which logic is defined by topology rather than geometry. The circuit is realized as a knitted textile formed from a single continuous yarn, where information is encoded in the topology of stitches and processed through controlled unraveling. By discretizing the textile into a lattice of interacting cells, we construct topological propagation rules that implement universal logic operations, including NOT, AND, and OR gates, as well as a half-adder. Experiments demonstrate that the logical output is robust against geometric deformation, while mechanical factors affect only if the computation can be executed. These results establish topology-defined computation as a model for information processing in textiles and other reconfigurable physical systems.