Demonstration of our LOS-bubble-finding algorithm, where the zero point of the LOS position is arbitrary. (a) Starting from the galaxy farthest away from the observer, g_i, we invert 𝒯(d_IGM) (Figure 5, the red dashed line) to estimate the distance between the galaxy and the nearest neutral IGM patch, D_i. We set the LOS bubble diameter, D_bubble=D_i, and the redshift of the back of the bubble, z_back=z_i, that is, the redshift of the first galaxy. We then mark all galaxies in front of g_i within D_bubble (orange dots) to be inside the same bubble as g_i. (b) We then step through the bubble toward the observer to update our estimate of D_bubble. For a galaxy g_i+n which is a distance d_{i, i+n} from galaxy g_i we estimate the distance of galaxy g_i+n from neutral IGM, D_i+n. If D_i+n+d_{i, i+n}>D_bubble we update D_bubble→D_i+n+d_{i, i+n}. (c) Once we have iterated through all galaxies contained within D_bubble and D_bubble converges, we continue iterating through all the galaxies in the line-of-sight in the same manner to find all the bubbles. In this example sightline we find two bubbles and their associated galaxies (orange galaxies on the left and green galaxies on the right, the remaining blue point is a galaxy between the two bubbles and is not considered to be inside a bubble).