The LS method is applied repeatedly for the 𝑏 = 0.25 initial condition in Fig. , where 𝑏 indicates the fraction of the total length that is black. Since we specify that leftmost segments should be cut when segment lengths are equal, a regular, left-to-right, pattern for cut locations emerges as each largest segment is divided in turn. After 𝑁 = 1, 3, 7, and 15 applications of the LS approach, the states in Fig. are "optimally mixed," i.e., all segments of the same color are equally sized. Mixing completely segregated initial conditions, which we refer to as single black-white conditions, such as for 𝑁 = 0 in Fig. , using the LS method always produces optimally mixed states when 𝑁 = 2 𝑘 -1 for positive integers 𝑘.