> Ateam of Japanese and Hungarian researchers have shown P. polycephalum can solve the Shortest Path Problem. When grown in a maze with oatmeal at two spots, P. polycephalum retracts from everywhere in the maze, except the shortest route connecting the two food sources.
> When presented with more than two food sources, P. polycephalum apparently solves a more complicated transportation problem. With more than two sources, the amoeba also produces efficient networks. In a 2010 paper, oatflakes were dispersed to represent Tokyo and 36 surrounding towns. P. polycephalum created a network similar to the existing train system, and "with comparable efficiency, fault tolerance, and cost". Similar results have been shown based on road networks in the United Kingdom and the Iberian peninsula (i.e., Spain and Portugal). Some researchers claim that P. polycephalum is even able to solve the NP-hard Steiner Minimum Tree Problem.
> As the slime mould does not have any nervous system that could explain these intelligent behaviours, there has been considerable interdisciplinary interest in understanding the rules that govern its behaviour. Scientists are trying to model the slime mold using a number of simple, distributed rules. For example, P. polycephalum has been modeled as a set of differential equations inspired by electrical networks. This model can be shown to be able to compute shortest paths. A very similar model can be shown to solve the Steiner tree problem. However, currently these models do not make sense biologically, as they for example assume energy conservation inside the slime mould. Living organisms consume food, so energy can not be conserved. To build more realistic models, more data about the slime mould's network construction needs to be gathered.
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> Moreover, it has been reported that plasmodia can be made to form logic gates, enabling the construction of biological computers. In particular, plasmodia placed at entrances to special geometrically shaped mazes would emerge at exits of the maze that were consistent with truth tables for certain primitive logic connectives. However, as these constructions are based on theoretical models of the slime mould, in practice these results do not scale to allow for actual computation. When the primitive logic gates are connected to form more complex functions, the plasmodium ceased to produce results consistent with the expected truth tables.