Interactive three-dimensional simulations & visualizations

Visualizing the beauty in physics and mathematics

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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.

Cell size: 1 px 2 px 4 px 6 px 8 px 12 px 16 px	Frame rate: 1 fps 2 fps 5 fps 10 fps 25 fps 50 fps
Acorn 🌰	Die hard 💀
Double gun pulsar 🔫	Glider 🛩️
Glider gun 🔫	Heavyweight spaceship 🚀
Lightweight spaceship 🚀	Mega showcase 🚨
Methusalah chaos 😵‍💫	Oscillator wall ⅏
Pentadecathlon 🏃🏻	Pentomino ⚅
Pulsar 🌟	Random 🎲

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 (yellow 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.

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