Figure 6

Revisit time analysis. For illustrative purposes we focus our analysis on the Craters map and four search strategies that have different exploration diffusivity levels (see Fig. 4). (a) A colour map representation of the time since last visit to each cell at step number 300K. An animated version of this representation (Supplementary Video 2) is also provided. Note the non-uniformity of the Brownian strategy in this representation. Markers 1, 2 and 3 indicate the location of three representative cells which are discussed below. The revisit sequence was also stored for every cell during a 100M step simulation for each strategy. (b) Cumulative distribution function (CDF) of the revisit intervals for every cell. There are three overlayed traces corresponding to the CDF for cells 1, 2 and 3. The ballistic strategy shows significantly increased redundancy near the search area limits (cell 3). (c) Revisit sequence for cell 2 on a plot where each data point is the revisit interval annotated at the corresponding simulation time step. The heterogeneous revisiting time of the Brownian strategy becomes apparent as it is the only strategy with revisit times \(>10^5\) (indicated by a vertical line) which translate into empty horizontal stripes. This effect can be overcome with the implementation of a short-term memory to reduce local repetitions (“Brownian, memory”), which yields similar temporal profile to the Lévy-mirror bounce strategy for this map. The ballistic strategy yields medium revisit times concentrated between \(10^3\) and \(10^5\).