4.2: Game of Life

Contents

4.2: Game of Life#

Learning objectives

  1. Understand the Concept of Emergence in Systems:

    • Identify how simple rules at the micro-level can lead to complex patterns at the macro-level.

    • Analyse how the Game of Life demonstrates emergence through patterns like spaceship, oscillators, and still life.

  2. Model Initialization and Boundary Conditions:

    • Understand the importance of initial conditions in determining system outcomes.

    • Recognize how boundary conditions (e.g., toroidal grids in the Game of Life) can impact system behaviour.

  3. Adaptability and Sensitivity Analysis:

    • Experiment with changing parameters (e.g., initial population density) to observe system sensitivity.

    • Assess how slight changes in initial configurations can lead to vastly different outcomes.

  4. Temporal Dynamics and Stability:

    • Observe how systems can stabilize (e.g., still life patterns) or become chaotic.

    • Understand the concept of equilibrium and oscillation within systems.

  5. Analyse Interactions and Dependencies:

    • Examine how agents interact with their neighbours and how local interactions can produce global patterns.

    • Recognize the dependencies between agents and how they can impact overall system behaviour.

Conway’s Game of Life model demonstrates a notable dynamic representative of cellular automata. Each cell within the grid follows simple rules based on its neighbours, leading to emergent patterns that evolve over time. The simulation begins with a random allocation of living cells on a grid. As each generation progresses, cells determine their future state - to either remain alive, die, or be reborn - based on the number of living neighbours they have. Over the course of the simulation, this can result in intricate patterns, oscillations, or even static formations. The agents will do their steps simultaneous, ensuring that all cells evaluate their next state based on the current state of their neighbours, preserving the integrity of Conway’s original design. The model’s dynamics, driven by these simple rules, can lead to unexpected and complex behaviours.

Read more about it in the Wikipedia article.

Watch this video.

Local birth and survival rules generate changing cell patterns.

Before you read what to expect, explore it for yourself. The board below is a live Game of Life, where a few simple rules about each cell’s neighbours decide whether it lives or dies from one tick to the next. Predict whether the shapes you place will settle into a still pattern, vanish, or set off across the board.

Learning Activity: Play Conway's Game of Life
get a feel for how simple neighbour rules produce moving, blinking, and growing patterns.
A live Game of Life board you can draw on, where each cell follows four rules based only on its eight neighbours: it survives with 2 or 3 live neighbours, a dead cell with exactly 3 comes to life, and everything else dies.
Click or drag on the board to draw live cells, or drop in a ready-made shape with the Glider, Pulsar, Blinker or Random buttons, then press Play.
generation 0alive 0
drop a shape:
Every cell here is an agent that looks only at its eight neighbours and applies the same four rules. Nothing tells the glider to move or the pulsar to beat: those patterns emerge from the local rules alone. In the exercises you will build this exact model in Mesa, with a grid of Cell agents, and see the same behaviour come out of your own code.

Key takeaways#

Key takeaways

  • Game of Life cells follow only local birth and survival rules, yet stable, oscillating, and moving patterns emerge.

  • Initial configuration matters, so comparing patterns is as important as changing rules.

  • The exercises connect grid states, time-series metrics, and visual evidence.

Begin with 4.2.1: Exercises to build, run, test, and extend the model.

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