Goles, E., Tsompanas, M. A., Adamatzky, A., Tegelaar, M., Wosten, H. A. B., & Martinez, G. J. (2020). Computational universality of fungal sandpile automata. Phys. Lett. A, 384(22), 8 pp.
Abstract: Hyphae within the mycelia of the ascomycetous fungi are compartmentalised by septa. Each septum has a pore that allows for intercompartmental and interhyphal streaming of cytosol and even organelles. The compartments, however, have special organelles, Woronin bodies, that can plug the pores. When the pores are blocked, no flow of cytoplasm takes place. Inspired by the controllable compartmentalisation within the mycelium of the ascomycetous fungi we designed twodimensional fungal automata. A fungal automaton is a cellular automaton where communication between neighbouring cells can be blocked on demand. We demonstrate computational universality of the fungal automata by implementing sandpile cellular automata circuits there. We reduce the Monotone Circuit Value Problem to the Fungal Automaton Prediction Problem. We construct families of wires, crossovers and gates to prove that the fungal automata are Pcomplete. (C) 2020 Elsevier B.V. All rights reserved.

Adamatzky, A., Goles, E., Martinez, G. J., Tsompanas, M. A., Tegelaar, M., & Wosten, H. A. B. (2020). Fungal Automata. Complex Syst., 29(4), 759–778.
Abstract: We study a cellular automaton (CA) model of information dynamics on a single hypha of a fungal mycelium. Such a filament is divided in compartments (here also called cells) by septa. These septa are invaginations of the cell wall and their pores allow for the flow of cytoplasm between compartments and hyphae. The septal pores of the fungal phylum of the Ascomycota can be closed by organelles called Woronin bodies. Septal closure is increased when the septa become older and when exposed to stress conditions. Thus, Woronin bodies act as informational flow valves. The onedimensional fungal automaton is a binarystate ternary neighborhood CA, where every compartment follows one of the elementary cellular automaton (ECA) rules if its pores are open and either remains in state 0 (first species of fungal automata) or its previous state (second species of fungal automata) if its pores are closed. The Woronin bodies closing the pores are also governed by ECA rules. We analyze a structure of the composition space of cellstate transition and porestate transition rules and the complexity of fungal automata with just a few Woronin bodies, and exemplify several important local events in the automaton dynamics.

Goles, E., Adamatzky, A., Montealegre, P., & RiosWilson, M. (2021). Generating Boolean Functions on Totalistic Automata Networks. Int. J. Unconv. Comput., 16(4), 343–391.
Abstract: We consider the problem of studying the simulation capabilities of the dynamics of arbitrary networks of finite states machines. In these models, each node of the network takes two states 0 (passive) and 1 (active). The states of the nodes are updated in parallel following a local totalistic rule, i.e., depending only on the sum of active states. Four families of totalistic rules are considered: linear or matrix defined rules (a node takes state 1 if each of its neighbours is in state 1), threshold rules (a node takes state 1 if the sum of its neighbours exceed a threshold), isolated rules (a node takes state 1 if the sum of its neighbours equals to some single number) and interval rule (a node takes state 1 if the sum of its neighbours belong to some discrete interval). We focus in studying the simulation capabilities of the dynamics of each of the latter classes. In particular, we show that totalistic automata networks governed by matrix defined rules can only implement constant functions and other matrix defined functions. In addition, we show that t by threshold rules can generate any monotone Boolean functions. Finally, we show that networks driven by isolated and the interval rules exhibit a very rich spectrum of boolean functions as they can, in fact, implement any arbitrary Boolean functions. We complement this results by studying experimentally the set of different Boolean functions generated by totalistic rules on random graphs.
