Self-aware and self-expressive physical systems are inspiring new methodologies for engineering solutions of complex computing problems. Among many other examples, the slime mold Physarum Polycephalum exhibits self-awareness and self-expressiveness while adapting to changes in its dynamical environment and solving resource-consuming problems like shortest path, proximity graphs or optimization of transport networks. As such, the modeling of the slime mold's behavior is essential when designing bio-inspired algorithms and hardware prototypes. The goal of this paper is to combine one of the powerful parallel computational tools, cellular automata (CA) with the adaptive potential of Physarum slime mold. Namely, we propose a CA model and multi-agent approach to imitate the behavior of the plasmodium. We then test the efficacy of the proposed model on graph problems such as the maze problem or the traveling salesman problem (TSP). Finally, the virtual Physarum model is evaluated on a data set for pattern recognition purposes and achieves to form very effectively the letters of the alphabet, especially when compared with real experiments performed to prove the efficacy of the proposed model. Furthermore, to exploit the CA's inherent parallelism and make the model's responses faster, both GPU and hardware implementations are proposed and compared. As a result, an accelerated virtual lab is developed which uses a multi-agent CA model to describe the behavior of plasmodium and can be used as an intelligent, autonomous, self-adaptive system in various heterogeneous and unknown environments spanning from different types of graph problems up to real life-time applications.