The LS method used here extracts half of the longest black segment and inserts it at the middle of the longest white segment. This is done by placing cuts at the middle and right edge of the longest black segment and the middle of the longest white segment. Configurations with multiple segments of equal length necessarily occur after each application of the LS method. When multiple segments share the longest length, we split the leftmost one, although splitting any of the equal length segments creates the same increase in the degree of mixing. On a periodic domain, all permutations of a 3-IET that can mix are identical to swapping the order of any two intervals (between cuts), i.e., there is no implicit ordering to the cut locations. However, we restrict ourselves to swapping the interior two intervals to make an equivalent IET without the periodic boundary. Thus, the LS method assigns a distinct purpose to each cut (black and white centers and an interface)-a helpful feature for clarifying the problem for ML. For example, in Fig. (a), the two species are each segregated into single segments. Three cuts (red triangles) specified by the LS method split the domain into three intervals [Fig. ments of each color [Fig. )]-a more mixed state than single segments of each color. Figures ) apply the LS method for one more step using the cuts labeled in Fig. ). The LS method always halves one of the largest features of the domain with each step.