First I just thought, “How weird! Applying many-valued logic to slime moulds.” But then I read it and not only is this a bona-fide application of p-adic logic to the behavior of slime moulds, no, the slime moulds are used as computers in this application! And my own work is used! So, yay to p-adic logic and slime mould computers!
Andrew Schumann, p-Adic valued logical calculi in simulations of the slime mould behaviour. J. Applied Non-Classical Logics 2015, forthcoming.
In this paper we consider possibilities for applying p-adic valued logic BL to the task of designing an unconventional computer based on the medium of slime mould (order Physarales, class Myxomecetes, subclass Myxogastromycetidae), the giant amoebozoa that looks for attractants and reaches them by means of propagating complex networks. If it is assumed that at any time step t of propagation the slime mould can discover and reach not more than \(p-1\) attractants, then this behaviour can be coded in terms of p-adic numbers. As a result, this behaviour implements some p-adic valued arithmetic circuits and can verify p-adic valued logical propositions.
[Image credit: Andrew Adamatzky, Physarum Machines (World Scientific, 2010), courtesy of Andrew Adamatzky]