🫀 Game of life

Conway’s game of life

Conway’s Game of Life illustrates the same principle as the Mandelbrot set, namely that complex structures can emerge from an astonishingly small and simple set of rules.

🎯 Illustration of TiledPlane view in Helion
🐍 A VPython demo is available as well, see game_of_life.py

Game of Life – 2D cellular automaton

This visualization shows Conway’s Game of Life, a simple mathematical model where complex behavior emerges from very simple rules.

The space is divided into a grid of cells. Each cell is either:

• alive (green pixel), or
• dead (black pixel).

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Rules of the game

At each time step, every cell updates simultaneously based on its eight neighbors:

1. A living cell survives if it has 2 or 3 living neighbors
2. A dead cell becomes alive if it has exactly 3 living neighbors
3. All other cells die or remain dead

These rules can be written as:

$$\text{alive}_{t+1}(x,y) \begin{cases} 1 & \text{if } n=3 \\ 1 & \text{if } n=2 \text{ and alive}_t=1 \\ 0 & \text{otherwise} \end{cases}$$

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What you observe

• Stable structures
• Oscillating patterns
• Moving objects (gliders)
• Chaotic growth from simple beginnings

No randomness is added after the start — all complexity emerges from the rules alone.

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Why this matters

The Game of Life is a classic example of:

• emergent behavior
• cellular automata
• how local rules can produce global structure

It appears in physics, biology, computer science, and artificial life research.