A Two-Player Game of Life

Abstract

We present a new extension of Conway's game of life for two players, which we call p2life. P2life allows one of two types of token, black or white, to inhabit a cell, and adds competitive elements into the birth and survival rules of the original game. We solve the mean-field equation for p2life and determine by simulation that the asymptotic density of p2life approaches 0.0362.

Urban encounters

“…This observation is crucial in developing a mathematical model describing human encounter. To derive such a model we can take an approach similar to the one described in [7], which involves assigning a probability to each possible value that a cell can have after n iterations of the game. From our analysis we have identified that this probability is disproportionately shifted in favour of the extreme possible values.…”

“…For example, Cunha et al explored this idea in [4] by mapping the location of sensor nodes into a 2D grid and using the energy level and state (whether the sensor node is active or in standby mode) of neighbouring nodes to determine a node's state at the next step of the simulation. A further adaptation [7] describes how a two-player Game of Life progresses under different player strategies.…”

ASAP: A framework for designing gamified models of complex systems

“…To illustrate the potential of ASAP as a (mobile) gamification tool, a two-player version of GoL [8], called p2life, has been implemented (see Fig. 6).…”

“…The rules of the gamified model are described in [8], where the asymptotic behavior of the system is analyzed. The first level model runs without human interplay, that is to say, the system starts from an initial population and its evolution continues without interactions.…”

“…In order to recognize patterns useful to predict and control the evolution of the system, the model allows the interaction between two players (each one controls a different species, recognized by shapes and colors) trying to overcome the opponent's population. In [8], authors claim to devise p2life into a game where players are allowed to make moves between generations, which change the configuration of the tokens, and devise strategies to overpower or live side-by-side with their opponent. The game starts from an initial configuration where each player's model sets randomly his agents in the world (coincident agents are removed from both groups).…”