Fungal Automata

💡 Research Summary

The paper introduces a novel computational model called “fungal automata” that abstracts the information dynamics occurring along a single hyphal filament of filamentous fungi. The biological basis of the model lies in the presence of septa—cross‑walls that partition the hypha into compartments—and the Woronin bodies that can block the pores of these septa, thereby regulating cytoplasmic flow. Each compartment (cell) is represented by a binary state (0 = absence of metabolites, 1 = presence of metabolites) and each septal pore by a binary valve state (0 = open, 1 = closed). The system is formalized as a one‑dimensional cellular automaton (CA) with a ternary neighbourhood (the cell itself and its immediate left and right neighbours). Two update rules are defined: a cell‑state transition rule f and a Woronin‑body transition rule g, both chosen from the 256 elementary cellular automata (ECA) rules identified by Wolfram.

Two species of fungal automata are distinguished. In automaton M₁, a closed pore forces the cell to become state 0 and prevents its neighbours from detecting any signal. In automaton M₂, a closed pore leaves the cell’s state unchanged, reflecting the biological observation that some metabolites can still diffuse through partially occluded septa. The authors explore the composition of the two rules, f ∘ g, by mapping every ordered pair (f,g) to a single ECA rule h. They construct the predecessor set P(h) = { (f,g) | f ∘ g = h } and analyse its size distribution. Rules such as 0 (in M₁) and 51 (in M₂) have the largest predecessor sets, whereas the complex class‑IV rule 110 has very few, indicating that random composition of two ECAs rarely yields a complex dynamics.

Further algebraic properties are examined. Diagonal compositions f ∘ f are trivial in M₁ (always yielding rule 0) but produce a limited set of 16 distinct rules in M₂. Commutativity holds only when f = g in M₁, while M₂ exhibits 32 768 commuting pairs. Associativity is scarce: only 0.027 % of all possible triples are associative in M₁ and 0.006 % in M₂. These findings delineate the structural constraints of rule composition in the fungal automaton framework.

To assess computational richness, the authors fix the cell‑state rule f to Wolfram’s class‑IV rule 110, known for universality and rich glider dynamics, and vary the Woronin rule g. They evaluate the Lempel–Ziv (LZ) compressibility of space‑time patterns as a proxy for complexity. In the first experimental series, a single cell (position n − 100) is equipped with a Woronin body that becomes active after 100 iterations. Among the 256 possible g‑rules, those with even decimal indices leave the dynamics unchanged, while the other half reduce LZ complexity by canceling gliders or simplifying glider‑gun behaviour. In the second series, Woronin bodies are placed periodically every 50 cells. Random initial conditions (density 0.3) evolve into patterns whose LZ complexity depends strongly on the chosen g‑rule. The highest complexities arise for g = 133 in M₁ and g = 193 in M₂, both of which sustain abundant gliders and glider guns. Mid‑range g‑rules produce mixed behaviours with fewer travelling localisations and growing homogeneous domains, while low‑complexity g‑rules quickly drive the system to stable, homogeneous states.

The paper also highlights local events enabled by Woronin bodies. A moving glider can be halted and converted into a stationary localisation when it encounters a closed pore, effectively implementing a memory cell. Regularly spaced Woronin bodies can act as “registers” that store bits of information, while the interaction of gliders with these bodies can generate oscillators or modify the period of glider guns, offering primitive logical gates and timing elements.

Overall, the study provides a rigorous mathematical and computational analysis of how a biologically motivated valve mechanism (Woronin bodies) can modulate the dynamics of a well‑studied complex CA (rule 110). By demonstrating that the presence, placement, and rule‑based behaviour of Woronin bodies can either preserve, simplify, or enrich the emergent patterns, the authors lay groundwork for the concept of “fungal intelligence” – distributed sensing and information processing in living mycelial networks. The work suggests that real fungal mycelia, with their natural septal occlusion mechanisms, could be harnessed as living substrates for unconventional computing, offering controllable pathways for signal propagation, memory storage, and logical operations within a biological substrate.