Fig. 3.

Folding an octahedron out of a linear chain. (A) Typical chain configurations that result after iterating Eq. 2. Numbers indicate the iteration number. Early on, the polymer configurations are dominated by thermal energy and random, yet as the interaction strengths increase and differentiate, more structured objects appear, and ultimately only the octahedron configuration exists (iterations 190–210). (B) Plotting the median percentage of deviation between the polymer’s radius of gyration $R_g$ and the radius of gyration for an octahedron $R_{\text{oct}}$ at each iteration shows that the optimizer again produces a monotonic decrease at each step, with an effectively exponential convergence in the last 30 iterations. By the last 10 iterations, the median deviation from a perfect octahedron is roughly 1%. (C) In plotting the coupling constants against iteration number, we find that the optimizer adjusts coupling constants in groups. It is clear that the active coupling constants form the contact network for an octahedron (C, Inset).