Slime mold Physarum polycephalum optimizes its foraging behaviour by minimizing the distances between the sources of nutrients it spans. When two sources of nutrients are present, the slime mold connects the sources, with its protoplasmic tubes, along the shortest path. We present a two-dimensional mesh grid memristor based model as an approach to emulate Physarum's foraging strategy, which includes space exploration and reinforcement of the optimally formed interconnection network in the presence of multiple aliment sources. The proposed algorithmic approach utilizes memristors and LC contours and is tested in two of the most popular computational challenges for Physarum, namely maze and transportation networks. Furthermore, the presented model is enriched with the notion of noise presence, which positively contributes to a collective behavior and enables us to move from deterministic to robust results. Consequently, the corresponding simulation results manage to reproduce, in a much better qualitative way, the expected transportation networks.