Emergent search strategies from the physics of fluid-driven branching

Biological search strategies in complex environments alternate between exploration and exploitation, and are suggestive of the behavior of a sentient organism. We demonstrate that a simple physical system, in which self-organized branched patterns form upon injection of a low-viscosity fluid into a Hele-Shaw cell containing a yield-stress fluid, might allow for a useful interpretation in terms of this complex behavioral strategy. As we inject water from a point source into a sealed cell with one point sink, the expansion of the branched pattern towards the sink appears to change from a direct (exploitative) to an indirect (exploration) strategy with an increase in flow-rate. We show that this transition is connected to a switch from a viscosity-dominated to an elasticity-dominated response from the yield-stress fluid to the invading fluid and that the corresponding flow-rate can be predicted. Moreover, we find that at this transition, the invasion strategy is most cost-effective in terms of the amount of material that needs to be displaced to reach the sink. Overall, our results suggest how a combination of local rules and global constraints in a mundane physical system can lead to concrete examples of embodied adaptation, exploration and learning.