Figure 2

Linked portions of open or closed curves: The linked region of two curves, Γ₁ and Γ₂ is defined as the shortest portion that, upon closure, has the same topology of the original physical link. For open curves, such region can be found by a stochastic top-down reduction of the chains from their termini, as illustrated here. The two panels pertain to physical links with the same topology, the Hopf or \({2}_{1}^{2}\) link, but with large differences for the length of their linked portion, which is indicated with a * subscript in the right part of the panels. For closed chains, the contour reduction can be started from randomly chosen points on the rings, see also Figs S1 and S2 in SI.