Computation through defect propagation in knitted fabrics

A knitted or crocheted fabric is a lattice of complex topology composed of a single strand of yarn. In our previous work, we introduced a topological framework to classify fabrics by their knittability, using the propagation of local defects. Here, we extend this concept to demonstrate a form of physical computation implemented entirely within a single yarn. Each logical bit is encoded by a pair of stitches, and computation proceeds through propagation of unravelling, which is governed solely by the topology of interlinked loops. We experimentally constructed NOT, AND, and OR gates, as well as half-adder circuits, showing that the logical outcomes remain invariant under large geometric deformations that preserve topology. Our results establish knitted fabrics as a model system for defect-driven information processing in slender matter, highlighting a new route by which dynamics of topology can transmit and transform information.