Extended Data Fig. 5: Image analysis of local and long-range order in the patterns.

a, SEM image of a trefoil pattern. b, Histogram representing a simple counting of the number of spokes in each unit cell. The dominant feature in the 12 μm × 17 μm SEM image in a is the three-spoke pattern. We also include in the histogram the number of unit cells that have missing pillars or other defects. c, A unit cell of the phase-field-simulated trefoil pattern. d, Mean unit cell obtained by averaging the intensity at each pixel from a false-coloured version of the SEM image in a. The experimental average matches the ideal simulated unit cell well. e, Map of deviation between the simulated trefoil pattern and each unit cell of the experimental image. The unit cells having the lowest deviation are denoted in blue and those with the greatest deviation in red. Cells where the template pillars appeared damaged were not included in the analysis. f, Unit cell of the simulated cinquefoil pattern. g, Averaged unit cell obtained from the SEM image shown in Extended Data Fig. 4c. h, Unit cell of the simulated hexafoil pattern. i, Averaged unit cell obtained from the SEM image shown in Extended Data Fig. 4e. All scale bars, 1 μm.