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During the last years, a well studied biological substrate, namely Physarum polycephalum, has been proven efficient on finding appropriate and efficient solutions in hard to solve complex mathematical problems. The plasmodium of P. polycephalum is a single-cell that serves as a prosperous bio-computational example. Consequently, it has been successfully utilized in the past to solve a variety of path problems in graphs and combinatorial problems. In this work, this interesting behaviour is mimicked by a robust unconventional computational model, drawing inspiration from the notion of Cellular and Learning Automata. Namely, we employ principles of Cellular Automata (CAs) enriched with learning capabilities to develop a robust computational model, able of modelling appropriately the aforementioned biological substrate and, thus, capturing its computational capabilities. CAs are very efficient in modelling biological systems and solving scientific problems, owing to their ability of incarnating essential properties of a system where global behaviour arises as an effect of simple components, interacting locally. The resulting computational tool, after combining CAs with learning capabilities, should be appropriate for modelling the behaviour of living organisms. Thus, the inherent abilities and computational characteristics of the proposed bio-inspired model are stressed towards the experimental verification of Physarum's ability to model Logic Gates, while trying to find minimal paths in properly configured mazes with food sources. The presented simulation results for various Logic Gates are found in good agreement, both qualitatively and quantitatively, with the corresponding experimental results, proving the efficacy of this unconventional bio-inspired model and providing useful insights for its enhanced usage in various computing applications.