Conway's Game of Life — 3D Lab Simulation
Paint cells, load a glider or the Gosper gun and watch complexity emerge from three simple rules
Theoretical Foundation & Historical Context
John Conway introduced the Game of Life in 1970 through Martin Gardner's Scientific American column. Each grid cell is alive or dead and all cells update simultaneously from their eight neighbours: a live cell survives with 2 or 3 neighbours, a dead cell is born with exactly 3. From this rule emerge still lifes, oscillators, travelling gliders and even glider guns; the game is Turing complete, so it can compute anything computable.
Law: Two-dimensional cellular automaton, rule B3/S23 | Scientist: John Horton Conway | Year: 1970
Key Learning Objectives & Competencies
- ✓ Apply the B3/S23 rule by hand to a small pattern and predict the next generation.
- ✓ Identify still lifes, oscillators and spaceships such as the glider.
- ✓ Explain how simple local rules produce complex global behaviour (emergence).
Mathematical Formulations & Differential Equations
s'(x,y) = 1 nếu n = 3, hoặc n = 2 và s = 1; ngược lại 0
n is the number of live cells among the 8 neighbours (Moore neighbourhood); notation B3/S23
n = Σ s(x+i, y+j), (i, j) ∈ {−1,0,1}² \ {(0,0)}
The grid here wraps around like a torus so it has no edge
ρ(g) = (số ô sống) / (cột × hàng)
From random soup, ρ usually falls and then settles near a few percent
Physical Parameters & Units of Measurement
| Symbol | Physical Quantity | SI Unit | Default |
|---|---|---|---|
| s | Cell state: 1 alive, 0 dead | — | — |
| n | Live neighbours in the Moore neighbourhood | — | — |
| g | Number of generations stepped | — | — |
| ρ | Density of live cells | — | — |
Real-World & Industrial Engineering Applications
Models of emergence and self-organisation in biology and physics.
Computability theory: Life can simulate a universal Turing machine.
Parallel computing and GPU stencil kernels use the same neighbour-update pattern.
3-Step Controlled Experimental Protocol
- Step 1: Baseline Setup — Initialize the simulation in standard conditions and observe undisturbed system dynamics.
- Step 2: Parameter Variation — Gradually modulate physical parameters using the control panel sliders.
- Step 3: Verification & Phase Space Analysis — Compare phase space trajectories and conservation metrics against analytical ODE solutions.
Frequently Asked Questions (FAQ)
Why is it called a game with no players?
After choosing the initial state, everything evolves by the rule; the user only picks the starting configuration and watches.
What is the Gosper glider gun?
A 36-cell oscillator with period 30 that emits one glider per cycle; found in 1970, it showed the population can grow without bound.
What happens at the grid edge?
The grid wraps: left joins right and top joins bottom, so a glider leaving one side re-enters from the opposite side.
Related Simulations & Experiments
Interactive Simulation: Interactive real-time 60 FPS WebGL simulation is active in your browser. Rotate, zoom, and inspect physical apparatus components with full camera freedom.