Related papers: The X-rule: universal computation in a non-isotrop…
We re-examine the isotropic Precursor-Rule (of the anisotropic X-Rule) and show that it is also logically universal. The Precursor-Rule was selected from a sample of biased cellular automata rules classified by input-entropy. These biases…
To respect physics and nature, cellular automata (CA) models of self-organisation, emergence, computation and logical universality should be isotropic, having equivalent dynamics in all directions. We present a novel paradigm, the iso-rule,…
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…
This paper describes a new concept of cellular automaton (CA). XCA consists of a set of arcs (edges) that correspond to cells in CA. At a particular time, the arcs are connected to a directed graph. With each time step, the arcs exchange…
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…
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…
We propose a four-way classification of two-dimensional semi-totalistic cellular automata that is different than Wolfram's, based on two questions with yes-or-no answers: do there exist patterns that eventually escape any finite bounding…
The B36/S125 (or "2x2") cellular automaton is one that takes place on a 2D square lattice much like Conway's Game of Life. Although it exhibits high-level behaviour that is similar to Life, such as chaotic but eventually stable evolution…
To understand the underlying principles of self-organisation and computation in cellular automata, it would be helpful to find the simplest form of the essential ingredients, glider-guns and eaters, because then the dynamics would be easier…
The cellular automaton (CA) pulsing model (arXiv:1806.06416) described the surprising phenomenon of spontaneous, sustained and robust rhythmic oscillations, pulsing dynamics, when random wiring is applied to a 2D `glider' rule running in a…
The cellular automata with local permutation invariance are considered. We show that in the two-state case the set of such automata coincides with the generalized Game of Life family. We count the number of equivalence classes of the rules…
This paper deals with the theory and application of 2-Dimensional, nine-neighborhood, null- boundary, uniform as well as hybrid Cellular Automata (2D CA) linear rules in image processing. These rules are classified into nine groups…
A cellular automata (CA) configuration is constructed that exhibits emergent failover. The configuration is based on standard Game of Life rules. Gliders and glider-guns form the core messaging structure in the configuration. The blinker is…
A Cellular Automata (CA) rule is presented that can generate "loop patterns" in a 2D grid under fixed boundary conditions. A loop is a cyclically closed path represented by one-cells enclosed by zero-cells. A loop pattern can contain…
Cellular automata (CA) are dynamical systems defined by a finite local rule but they are studied for their global dynamics. They can exhibit a wide range of complex behaviours and a celebrated result is the existence of (intrinsically)…
This paper introduces Differentiable Logic Cellular Automata (DiffLogic CA), a novel combination of Neural Cellular Automata (NCA) and Differentiable Logic Gates Networks (DLGNs). The fundamental computation units of the model are…
A cellular automaton collider is a finite state machine build of rings of one-dimensional cellular automata. We show how a computation can be performed on the collider by exploiting interactions between gliders (particles, localisations).…
We propose the characterization of binary cellular automata using a set of behavioral metrics that are applied to the minimal Boolean form of a cellular automaton's transition function. These behavioral metrics are formulated to satisfy…
Cellular automata (CA) have been utilized for decades as discrete models of many physical, mathematical, chemical, biological, and computing systems. The most widely known form of CA, the elementary cellular automaton (ECA), has been…
Modeling the ability of multicellular organisms to build and maintain their bodies through local interactions between individual cells (morphogenesis) is a long-standing challenge of developmental biology. Recently, the Neural Cellular…