Related papers: Embedding arbitrary Boolean circuits into fungal a…
We consider the problem of embedding odometers in one-dimensional cellular automata. We show that (1) every odometer can be be embedded in a gliders with reflecting walls cellular automaton, which one depending on the odometer, and (2) an…
This article is set in the field of regulation networks modeled by discrete dynamical systems. It focuses on Boolean automata networks. In such networks, there are many ways to update the states of every element. When this is done…
In a probabilistic cellular automaton in which all local transitions have positive probability, the problem of keeping a bit of information indefinitely is nontrivial, even in an infinite automaton. Still, there is a solution in 2…
Many dynamical systems can be naturally represented as `Bratteli-Vershik' (or `adic') systems, which provide an appealing combinatorial description of their dynamics. If an adic system X satisfies two technical conditions (`focus' and…
We define a cellular automaton where a resting cell excites if number of its excited neighbours belong to some specified interval and boundaries of the interval change depending on ratio of excited and refractory neighbours in the cell's…
The derivatives of a Boolean function are defined up to any order. The Taylor and MacLaurin expansions of a Boolean function are thus obtained. The last corresponds to the ring sum expansion (RSE) of a Boolean function, and is a more…
We consider random boolean cellular automata on the integer lattice, i.e., the cells are identified with the integers from 1 to $N$. The behaviour of the automaton is mainly determined by the support of the random variable that selects one…
Quantum cellular automata are alternative quantum-computing paradigms to quantum Turing machines and quantum circuits. Their working mechanisms are inherently automated, therefore measurement free, and they act in a translation invariant…
An automata network is a finite graph where each node holds a state from some finite alphabet and is equipped with an update function that changes its state according to the configuration of neighboring states. More concisely, it is given…
We classify quantum cellular automata whose cells are qubits, on hypercubic lattices $\mathbb Z^s$, with the von Neumann neighborhood scheme, in terms of realizability as finite-depth quantum circuits. We show the most general structure of…
In the 1980's Stallings showed that every finitely generated subgroup of a free group is canonically represented by a finite minimal immersion of a bouquet of circles. In terms of the theory of automata, this is a minimal finite inverse…
A Boolean function $f$ on $k$~bits induces a shift-invariant vectorial Boolean function $F$ from $n$ bits to $n$ bits for every $n\geq k$. If $F$ is bijective for every $n$, we say that $f$ is a proper lifting, and it is known that proper…
We say that a Cellular Automata (CA) is coalescing when its execution on two distinct (random) initial configurations in the same asynchronous mode (the same cells are updated in each configuration at each time step) makes both…
We created two dimensional hexagonal cellular automata to obtain complexity. Considering the game of life rules, Wolfram's works about life-like structures and John von Neumann's self-replication, self-maintenance, self-reproduction…
The Game of Life cellular automaton is a classical example of a massively parallel collision-based computing device. The automaton exhibits mobile patterns, gliders, and generators of the mobile patterns, glider guns, in its evolution. We…
In this work, we investigate the computational aspects of asynchronous cellular automata (ACAs), a modification of cellular automata in which cells update independently, following an asynchronous schedule. We introduce flip automata…
We present a novel form of Liquid Automata, using this to simulate autopoiesis, whereby living machines self-organise in the physical realm. This simulation is based on an earlier Cellular Automaton described by Francisco Varela. The basis…
Factorized dynamics in soliton cellular automata with quantum group symmetry is identified with a motion of particles and anti-particles exhibiting pair creation and annihilation. An embedding scheme is presented showing that the…
The emergence of complex behaviors in cellular automata is an area that has been widely developed in recent years with the intention to generate and analyze automata that produce space-moving patterns or gliders that interact in a periodic…
Cellular automata are a set of computational models in discrete space that have a discrete time evolution defined by neighbourhood rules. They are used to simulate many complex systems in physics and science in general. In this work,…