Related papers: Cultivating the Garden of Eden
We investigate the allowed configurations in the stationary state of the cellular automaton model for single-lane traffic. It is found that certain states in the configuration space can not be reached if one uses parallel dynamics. These…
Suppose $\tau$ is a cellular automaton over an amenable group and a finite alphabet. Celebrated Garden of Eden theorem states, that pre-injectivity of $\tau$ is equivalent to non-existence of Garden of Eden configuration. In this paper we…
We prove the Garden of Eden theorem for cellular automata with finite set of states and finite neighbourhood on right amenable left homogeneous spaces with finite stabilisers. It states that the global transition function of such an…
The basis for most of the ideas mentioned in this paper is the theory of cellular automata. A cellular automata contains a regular grid of cells, with each cell having a pre-defined set of finite states. The initial state is determined at…
Conway's Game of Life is the best-known cellular automaton. It is a classic model of emergence and self-organization, it is Turing-complete, and it can simulate a universal constructor. The Game of Life belongs to the set of semi-totalistic…
Autonomous threshold element circuit networks are used to investigate the structure of neural networks. With these circuits, as the transition functions are threshold functions, it is necessary to consider the existence of sequences of…
We prove that in the Game of Life, if the thickness-four zero-padding of a rectangular pattern is not an orphan, then the corresponding finite-support configuration is not a Garden of Eden, and that the preimage of every finite-support…
Conway's Game of Life (GOL) is a cellular automaton that has captured the interest of hobbyists and mathematicians alike for more than 50 years. The Game of Life is Turing complete, and people have been building increasingly sophisticated…
Conway's Game of Life (Life), a well known algorithm within the broader class of cellular automata (CA), exhibits complex emergent dynamics, with extreme sensitivity to initial conditions. Modeling and predicting such intricate behavior…
We establish several extensions of the well-known Garden of Eden theorem for non-uniform cellular automata over the full shifts and over amenable group universes. In particular, our results describe quantitatively the relations between the…
The Game of Life (GoL), one well known 2D cellular automaton, does not typically ensure interesting long-term phenotypic dynamics. Therefore, while being Turing complete, GoL cannot be said to be open-ended. In this work, we extend GoL with…
Cellular automata (CA) captivate researchers due to teh emergent, complex individualized behavior that simple global rules of interaction enact. Recent advances in the field have combined CA with convolutional neural networks to achieve…
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…
The classical "game of life" (GOL) due to Conway is a famous mathematical game constructed as a two-dimensional cellular automaton in which each cell is either alive or dead. A set of evolutionary rules determines whether a cell dies,…
In this paper we analyze Garden-of-Eden (GoE) states and fixed points of monotone, sequential dynamical systems (SDS). For any monotone SDS and fixed update schedule, we identify a particular set of states, each state being either a GoE…
This paper presents a probabilistic extension of the well-known cellular automaton, Game of Life. In Game of Life, cells are placed in a grid and then watched as they evolve throughout subsequent generations, as dictated by the rules of the…
Many decision problems concerning cellular automata are known to be decidable in the case of algebraic cellular automata, that is, when the state set has an algebraic structure and the automaton acts as a morphism. The most studied cases…
Without loss of generalisation to other systems, including possibly non-deterministic ones, we demonstrate the application of methods drawn from algorithmic information dynamics to the characterisation and classification of emergent and…
Conway's cellular automaton Game of LIFE has been conjectured to be a critical (or quasicritical) dynamical system. This criticality is generally seen as a continuous order-disorder transition in cellular automata (CA) rule space. LIFE's…
We define rules for cellular automata played on quasiperiodic tilings of the plane arising from the multigrid method in such a way that these cellular automata are isomorphic to Conway's Game of Life. Although these tilings are nonperiodic,…