Computational universality of fungal sandpile automata

Hyphae within the mycelia of the ascomycetous fungi are compartmentalised by septa. Each septum has a pore that allows for inter-compartmental and inter-hyphal 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 two-dimensional 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, cross-overs and gates to prove that the fungal automata are P-complete

Majority Adder Implementation by Competing Patterns in Life-Like Rule B2/S2345

In this paper we present a two-dimensional chaotic cellular automaton, the Life rule B2/S2345, able to simulate the action of an adder with majority gates, stimulated by gliders collisions transformed as competing patterns. Values of Boolean variables are encoded into two types of patterns --- symmetric (FALSE) and asymmetric (TRUE) patterns -- which compete for the `empty' space when propagate in the channels. We construct basic logical gates and elementary arithmetical circuits by simulating logical signals with gliders reaction propagating geometrically restricted by stationary non-destructible still life. Therefore an implementation of universal logical gates and a majority binary adder is constructe

A computation-universal two-dimensional 8-state triangular reversible cellular automaton

A reversible cellular automaton (RCA) is a cellular automaton (CA) whose global function is injective and every con guration has at most one predecessor. Margolus showed that there is a computation-universal two-dimensional 2-state RCA. But his RCA has nonuniform neighbor, so Morita and Ueno proposed 16-state computation-universal RCA using partitioned cellular automata (PCA). Because PCA can be regarded as a subclass of standard CA, their models has standard neighbor. In this paper, we show that the number of states of Morita and Ueno's models can be reducible. To decrease the number of states from their models with preserving isotropic and bit-preserving properties, we usedtriangular 3neighbor, and thus 8-state RCA can be possible. This is the smallest state two-dimensional RCA under the condition of isotropic property on the framework of PCA. We show that our model can simulate basic circuit elements such as unit wires, delay elements, crossing wires, switch gates and inverse switch gates. And it is possible to construct a Fredkin gate by combining these elements. Since Fredkin gate is known to be a universal logic gate, our model has computation-universality

Genetic evolution and equivalence of some complex systems: fractals, cellular automata and lindenmayer systems

Tesis doctoral inédita leída en la Universidad Autónoma de Madrid. Escuela Politécnica Superior, Departamento de Ingeniería informática.26-04-200