Extended Data Fig. 7: Scaling behavior of coarsening simulated with \(D_R = \frac{1}{{\sqrt R }}\) and \(D_R = \frac{1}{{2R}}\).

a, To test how the relation between α and β changes depending on the scaling of D_R with R, step size was scaled with R^−0.5. As in Fig. 3, values of α were chosen ranging from 0.1 to 1 with 20 replicates per condition, and droplets were merged over 10⁴ timesteps. Average radius of droplets in each replicate was averaged for each condition over 20 replicates and plotted. Shaded error bar reflects standard error of the mean. Power laws were fit between 10² and 5 × 10³ timesteps. b, The best-fit coarsening exponent β was plotted against the input α for each condition and fit with a line passing through the origin (0,0), yielding a slope of 0.40. c. To test whether a non-trivial number of mergers were missed in the simulation conditions in Fig. 3, simulations were repeated with halved step size (that is, \(D_R = \frac{1}{{2R}}\) instead of \(D_R = \frac{1}{R}\)). The dynamics are quite similar, demonstrating increasing coarsening exponent with increasing subdiffusive exponent, suggesting that mergers are rarely missed in the original simulation. d, With halved step size, relation between coarsening and diffusive exponent is similar (0.28, blue reference line) to simulations in Fig. 3 (0.3), as well as to theoretical prediction (0.33).