## 3 Methods
### Initialization and Simulation Rules
This tends to produce universes in the new space \(E_{k+1}\) of the highest possible quality. One might think that all the simulated universes converge to the same point, which would defeat the goal of maintaining sufficient diversity among our population of universes, but this is not observed, for two reasons: our Hooke's law repulsion disallows all bacteria to simultaneously move to an ideal position; and each universe may have a different number of bacteria since, if a real bacterium has split into two daughter cells between frames \(i\) and \(i+1\) and the split is not clear, some universes may choose to model this as one bent bacterium and others may decide a split has occured, and the two cases may equally well fit the observations. This step may require modification for more complex systems. Because of the design of our simulation, the best-fitting universe at \(t_{k+1}\) may not have come from the best-fitting universe at time \(t\). This means that the sequence of best-fitting universes may not form a consistent set representing the evolution of one possible universe. In particular, we have observed that, while following a sequence of best-fitting universes from frame-to-frame, it can sometimes occur that two bacteria at time \(t_{k}\) reunite into one bacterium in frame \(t_{k+1}\); this is, of course, impossible in the real world (and therefore never happens in any one of our simulated universes), and visually happens only because the best frame at \(t_{k+1}\) did not come from the best-fitting one at time \(t_{k}\). However, every universe at time \(t_{k+1}\) came from _some_ universe at \(t_{k}\), so continuity can be constructed by following a universe backwards in time. Accordingly, so as to be able to generate consistent lineage  
Figure 3: **Schematic diagram of method**: We depict moving from frame 40 to frame 41 of the video, with time \(t\) labeled along the horizontal axis. The disk represents a small volume element inside the high-dimensional “phase space” containing all relevant measures of the system being tracked. The green dot in the center of the disk represents “reality” (e.g., positions + orientations of all cells), and the size of the disk represents the extent of observational error (e.g., video resolution). All points inside the disk thus represent plausible measurements of the real system to within observational uncertainty. The black dots are the “ensemble” of simulated universes, all assumed to be within observational uncertainty of the real system. The second, largest disk represents the expansion of the ensemble to many plausible futures—many more universes than we had at frame 40, all of them plausible future trajectories of the system, and now occupying a space much larger than the video uncertainty. Between the 2 nd and 3 rd disks, we perform a “pulling” operation on all the universes, by performing a preliminary fit of each one to video frame 41, which pulls them all “closer” to the reality depicted in frame 41. However, even after this pulling stage, some members of the ensemble remain implausible—outside the measurement uncertainty of video frame 41. These are discarded, giving the smaller disk at the end of the pulling stage, which is then propagated to frame 41. Finally, if there are too many members of the ensemble that remain at frame 41, we take a final sample of the “best-fitting” members to initialize the process at frame 41.  
trees, we can construct a single universe that is consistent from the beginning to the end of the video by selecting any universe at the end and tracing it backwards through time to frame 0. The traceback stage also helps address ambiguity introduced by inconsistent or poor segmentation. Suppose, for example, frame \(k\) is properly segmented, \(k+1\) is over-segmented, and \(k+2\) is properly segmented. In that case, the \"correct\" universe--that is, the universe most closely corresponding to reality--will simply fail to be the best universe at \(k+2\).