Related papers: Conway's Game of Life is Omniperiodic
We investigate a special class of cellular automata (CA) evolving in a environment filled by an electromagnetic wave. The rules of the Conway's Game of Life are modified to account for the ability to retrieve life-sustenance from the field…
We integrate dual-process theories of human cognition with evolutionary game theory to study the evolution of automatic and controlled decision-making processes. We introduce a model where agents who make decisions using either automatic or…
Evolutionary dynamics provides an iconic relationship --- the periodic frequency of a game is determined by the payoff matrix of the game. This paper reports the first experimental evidence to demonstrate this relationship. Evidence comes…
Taking the absolute value of consecutive differences of a cyclicly ordered list of integers constitutes a simple dynamical system. For lists of lenght a power of two the process will terminate in all zeros, but examples with arbitarily long…
This brief paper describes the single-player card game called "Perpetual Motion" and reports on a computational analysis of the game's outcome. The analysis follows a Monte Carlo methodology based on a sample of 10,000 randomly generated…
We present what we argue is the generic generalization of Conway's "Game of Life" to a continuous domain. We describe the theoretical model and the explicit implementation on a computer.
A linear oscillator very weakly coupled with the object quantum system is proposed as a detector measuring the lifetime of irreversibility exhibited by the system, and classically chaotic coupled kicked rotors are examined as ideal…
In this paper, we present the simulation of a simple, yet significantly powerful, sequential model by cellular automata. The simulated model is called oblivious multi-head one-way finite automata and is characterized by having its heads…
Many natural processes occur over characteristic spatial and temporal scales. This paper presents tools for (i) flexibly and scalably coarse-graining cellular automata and (ii) identifying which coarse-grainings express an automaton's…
Several modifications of the famous mathematical Game of Life are introduced by making Game of Life rules stochastic and mutual influence of cells in their 8-neighborhood on a rectangular lattice spatially non-uniform. Results are reported…
We study one-dimensional cellular automata evolutions with both temporal and spatial periodicity. The main objective is to investigate the longest temporal periods among all two-neighbor rules, with a fixed spatial period $\sigma$ and…
Infinite games where several players seek to coordinate under imperfect information are known to be intractable, unless the information flow is severely restricted. Examples of undecidable cases typically feature a situation where players…
Recent experiments by Springer and Kenyon have shown that a deep neural network can be trained to predict the action of $t$ steps of Conway's Game of Life automaton given millions of examples of this action on random initial states.…
Many intracellular processes continue to oscillate during the cell cycle. Although it is not well-understood how they are affected by discontinuities in the cellular environment, the general assumption is that oscillations remain robust…
Real-world examples of periods of periodical organisms range from cicadas whose life-cycles are larger prime numbers, like 13 or 17, to bamboos whose periods are large multiples of small primes, like 40 or even 120. The periodicity is…
For non-monotone single and two-populations time-dependent Mean-Field Game systems we obtain the existence of an infinite number of branches of non-trivial solutions. These non-trivial solutions are in particular shown to exhibit an…
This is an introduction into John Conway's beautiful Combinatorial Game Theory, providing precise statements and detailed proofs for the fundamental parts of his theory. (1) Combinatorial game theory, (2) the GROUP of games, (3) the FIELD…
We have proposed two new evolutionary rules on spatio-iterated games that is not mimic evolution of strategies, and mainly discussed the Prisoner's Dilemma game \cite{toyota2} by the two evoutionary rules \cite{toyota3}. In this paper we…
Computational power can be measured by assigning an algebraic structure to a computational device. Here, we convert a small patch of Conway's Game of Life into a transformation semigroup. The conversion captures not only time evolution but…
An average-time game is played on the infinite graph of configurations of a finite timed automaton. The two players, Min and Max, construct an infinite run of the automaton by taking turns to perform a timed transition. Player Min wants to…