Simulation of Expected Results
Our proposed sorting mechanism depends very heavily on a particular random-walking mechanism that has not been demonstrated in literature before. The verification of this mechanism is thus a vital step in our research. Verification of the random walk in one dimension is fairly straightforward: as discussed in <LINK TO THE EXPERIMENTAL DESIGN SECTION>, a one-dimensional track is easy to construct, and will behave like a standard 1D random walk, showing an average translation on the order of after n steps. Thus, we should expect the time it takes to get to some specific level of fluorescence to be proportional to the square of the number of steps we start the walker from the irreversible substrate. If we can, in an experiment, record the fluorescence over time when the walker is planted at different starting points and show that that fluorescence varies by this relationship, we'll have fairly certainly verified one-dimensional random walking.
As a control for the verification of 2D random walking, we need to get some kind of an idea how long the random walk should take, and how that time will change distance as we start the walker at different points on the origami. This is particularly important information to get, seeing as our particular case of random walking is distinct from most of the other 2D random walks that have been studied -- our walker can only move to 4 of 6 surrounding locations due to the way it moves. Rather than mathematically investigating this system, I opted to just simulate it with a set of movement rules derived from our design. I also use the same basic simulation (with a few alterations and extra features) to simulate our entire sorting system in a one-cargo, one-goal scenario, to give us some rudimentary numbers on how long sorting should take, with one vs multiple walkers.