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Neural Cellular Automata (NCAs) are bio-inspired dynamical systems in which identical cells iteratively apply a learned local update rule to self-organize into complex patterns, exhibiting regeneration, robustness, and spontaneous dynamics.…
It is known that no-boundary Cellular Automata (CA) defined by bipermutive local rules give rise to Latin squares. In this paper, we study under which conditions the Latin square generated by a bipermutive CA is self-orthogonal, i.e.…
Individual cellular automata rules are attractive models for a range of biological and physical self-assembling systems. While coexpression and coevolution are common in such systems, ensembles of cellular automata rules remain poorly…
We show that a behaviour analogous to degenerate hyperbolicity can occur in nearest-neighbour cellular automata (CA) with three states. We construct a 3-state rule by "lifting" elementary CA rule 140. Such "lifted" rule is equivalent to…
Here I describe a view of the evolution of cellular automata that allows to operate on larger structures. Instead of calculating the next state of all cells in one step, the method here developed uses a time slice that can proceed at…
A square lattice distribution of coupled oscillators that have heteroclinic cycle attractors is studied. In this system, we find a novel type of patterns that is spatially disordered and periodic in time. These patterns are limit cycle…
We extend Cellular Automata to time-varying discrete geometries. In other words we formalize, and prove theorems about, the intuitive idea of a discrete manifold which evolves in time, subject to two natural constraints: the evolution does…
We present a probabilistic 3D generative model, named Generative Cellular Automata, which is able to produce diverse and high quality shapes. We formulate the shape generation process as sampling from the transition kernel of a Markov…
Cellular automata (CA) consist of an array of identical cells, each of which may take one of a finite number of possible states. The entire array evolves in discrete time steps by iterating a global evolution G. Further, this global…
We redefine the transition function of elementary cellular automata (ECA) in terms of discrete operators. The operator representation provides a clear hint about the way systems behave both at the local and the global scale. We show that…
We study the dynamics of the Rule 150 reversible cellular automaton (RCA). This is a one-dimensional lattice system of binary variables with synchronous (Floquet) dynamics, corresponding to a bulk deterministic and reversible discrete…
This paper presents a new framework for asynchrony. This has its origins in our attempts to better harness the internal decision making process of cellular automata (CA). Thus, we show that a max-plus algebraic model of asynchrony arises…
Probabilistic cellular automata describe the dynamics of classical spin models, which, for sufficiently small temperature $T$, can serve as classical memory capable of storing information even in the presence of nonzero external magnetic…
This study concerns the issue of high dimensional outliers which are challenging to distinguish from inliers due to the special structure of high dimensional space. We introduce a new notion of high dimensional outliers that embraces…
Multiple scattering theory is applied to the study of clusters of point-like scatterers attached to a thin elastic plate and arranged in quasi-periodic distributions. Two type of structures are specifically considered: the twisted bilayer…
Social discrimination seems to be a persistent phenomenon in many cultures. It is important to understand the mechanisms that lead people to judge others by the group to which they belong, rather than individual qualities. It was recently…
Central to the artificial life endeavour is the creation of artificial systems spontaneously generating properties found in the living world such as autopoiesis, self-replication, evolution and open-endedness. While numerous models and…
In previous works, hexagonal cellular automata (CA) have been studied as a variation of the famous Game of Life CA, mainly for spiral phenomena simulations; where the most interesting constructions are related to the Belousov-Zhabotinsky…
In this thesis we will work under the premises of the Cellular Automata Interpretation of QM, by Gerard 't Hooft, according to whom particles evolve following the rules of Cellular Automata (CA), a mathematical model consisting of discrete…
We explore the dynamics of a one-dimensional lattice of state machines on two states and two symbols sequentially updated via a process of "reflexive composition." The space of 256 machines exhibits a variety of behavior, including…