Fig. 1.

Discovery of privileged topologies. The two-tier strategy to detect admissible topologies consists of an initial Monte Carlo sampling of closed constructs made of n_T = 3, 4, 5 helical templates followed by an a posteriori selection of the quasi-planar, cyclic-symmetric and knotted instances. In this n_T = 5 example, the ensemble generated with unrestricted crankshaft moves includes two such instances: the 10₁₂₄ and the 5₁ knots. For visual clarity, here and in other figures the attractive patches joining the helical templates (discretised as chains of beads) are shown as white beads larger than their actual size