We present a new Life-like cellular automaton (CA) capable of logic universality -- the X-rule. The CA is 2D, binary, with a Moore neighborhood and $λ$ parameter similar to the game-of-Life, but is not based on birth/survival and is non-isotropic. We outline the search method. Several glider types and stable structures emerge spontaneously within X-rule dynamics. We construct glider-guns based on periodic oscillations between stable barriers, and interactions to create logical gates.
We present a new spontaneously emergent glider-gun in a 2D Cellular Automaton and build the logical gates NOT, AND and OR required for logical universality. The Ameyalli-rule is not based on survival/birth logic but depends on 102 isotropic neighborhood groups making an iso-rule, which can drive an interactive input-frequency histogram for visualising iso-group activity and dependent functions for filtering and mutation. Neutral inputs relative to logical gates are identified which provide an idealized striped-down form of the iso-rule.
Fuzzy cellular automaton is a dynamical system with a continuous state value embedding a cellular automaton with a discrete state value. We investigate a fuzzy cellular automaton obtained from an elementary cellular automaton of rule number 38. Its asymptotic solutions are classified into two types. One is a solution where stable propagating waves exist, and the other is a static uniform solution of constant value.
In this paper, we present stochastic synchronous cellular automaton defined on a square lattice. The automaton rules are based on the SEIR (susceptible $\to$ exposed $\to$ infected $\to$ recovered) model with probabilistic parameters gathered from real-world data on human mortality and the characteristics of the SARS-CoV-2 disease. With computer simulations, we show the influence of the radius of the neighborhood on the number of infected and deceased agents in the artificial population. The increase in the radius of the neighborhood favors the spread of the epidemic. However, for a large rang…
In this paper, we give a singular function on a unit interval derived from the dynamic of the one-dimensional elementary cellular automaton Rule 150. We describe properties of the resulting function, that is strictly increasing, uniformly continuous, and differentiable almost everywhere, and we show that it is not differentiable at dyadic rational points. We also give functional equations that the function satisfies, and show that the function is the only solution of the functional ones.
In this paper, we prove that there is a strongly universal cellular automaton in the dodecagrid, the tesselllation {5,3,4} of the hyperbolic 3D space, with four states but, it is not rotation invariant as the automaton of arXiv:2104.01561 is with five states. The present paper is not an improvement of arXiv:2104.01561. The reduction to four states of the automaton of the present paper results from a relaxation of the condition of rotation invariance. However, the relaxation is not complete: the rules are invariant with respect to rotations of the dodecahedron which leave it globally invariant …
We describe a cellular-automaton based, two-dimensional (2D) lattice model which generates global oscillations in the EEG spectrum as well as time series of local field potentials resembling those observed during slow wave sleep. This is made possible by the presence of pacemakers (local oscillators) which can be spontaneously ignited and whose activity propagates through space to synchronize all connected nodes.
In this paper we study the space evolution in the Rule 54 reversible cellular automaton, which is a paradigmatic example of a deterministic interacting lattice gas. We show that the spatial translation of time configurations of the automaton is given in terms of local deterministic maps with the support that is small but bigger than that of the time evolution. The model is thus an example of space-time dual reversible cellular automaton, i.e. its dual is also (in general different) reversible cellular automaton. We provide two equivalent interpretations of the result; the first one relies on t…
