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 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 one dimensional fungal automata is a binary
state ternary neighbourhood CA, where every compartment follows one of the
elementary cellular automata (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 analyse a structure of the
composition space of cell-state transition and pore-state transitions rules,
complexity of fungal automata with just few Woronin bodies, and exemplify
several important local events in the automaton dynamics
