Related papers: Fixed Point Constructions in Tilings and Cellular …
In this paper, we examine some properties of the fixed point set of a digitally continuous function. The digital setting requires new methods that are not analogous to those of classical topological fixed point theory, and we obtain results…
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…
The Tile Automata (TA) model describes self-assembly systems in which monomers can build structures and transition with an adjacent monomer to change their states. This paper shows that seeded TA is a non-committal intrinsically universal…
Cellular automata represent physical systems where both space and time are discrete, and the associated physical quantities assume a limited set of values. While previous research has applied cellular automata in modeling chemical,…
We consider fixed-point models for topological phases of matter formulated as discrete path integrals in the language of tensor networks. Such zero-correlation length models with an exact notion of topological invariance are known in the…
In this paper we study the existence and uniqueness of fixed points of a class of mappings defined on complete, (sequentially compact) cone metric spaces, without continuity conditions and depending on another function.
Finite automata were used to determine multiple addresses in number systems and to find topological properties of self-affine tiles and finite type fractals. We join these two lines of research by axiomatically defining automata which…
This paper presents a novel neural network architecture featuring automatic fixation point selection, designed to efficiently address complex tasks with reduced network size and computational overhead. The proposed model consists of: a…
We use the method of monotone iterations to obtain fixed point and coupled fixed point results for mixed monotone operators in the setting of partially ordered sets, with no additional assumptions on the partial order and with no…
Nonexpansive mappings play a central role in modern optimization and monotone operator theory because their fixed points can describe solutions to optimization or critical point problems. It is known that when the mappings are sufficiently…
We consider a solution of automata similar to Population Protocols and Network Constructors. The automata (or nodes) move passively in a well-mixed solution and can cooperate by interacting in pairs. Every such interaction may result in an…
Calibration of fixtures in robotic work cells is essential but also time consuming and error-prone, and poor calibration can easily lead to wasted debugging time in downstream tasks. Contact-based calibration methods let the user measure…
We study fixed points of cellular automata with $N$ sites on random sparse graphs. In the large $N$ limit such models are known to exhibit phase transitions, from a ``frozen'' phase, where at most a finite number of sites fluctuate at long…
Cellular automata (CA) are discrete-time dynamical systems with local update rules on a lattice. Despite their elementary definition, CA support a wide spectrum of macroscopic phenomena central to statistical physics: equilibrium and…
Cellular automata are computers, similar to Turing machines. The main difference is that Turing machines use a one-dimensional tape, whereas cellular automata use a two-dimensional grid. The best-known cellular automaton is the Game of…
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,…
We present an algorithm for constructing the fixed point of a general non-isometric similarity of the plane.
One-dimensional cellular automata are discrete dynamical systems that operate on an infinite lattice of sites and are characterized by the locality and uniformity of their update rule. Permutations of the state set and isometric…
In this paper, considering a wider class of simulation functions some fixed point results for multivalued mappings in $\alpha$-complete metric spaces have been presented. Results obtained in this paper extend and generalize some well-known…
We develop new tools for the construction of fixed point sets in digital topology. We define excludable points and show that these may be excluded from all freezing sets. We show that articulation points are excludable. We also present…