Nodal Tangles

We study piecewise linear knot diagrams in the base of almost toric fibrations of symplectic four-manifolds. These diagrams translate to deformations of the almost toric fibration. We give several applications to symplectic topology, among them a proof of a conjecture by Symington, the calculation of the displacement energy for many fibres of toric moment maps, and an elementary recipe for building and distinguishing Lagrangian torus knots.