The Beauty of Cellular Automata

If you’ve visited my homepage, you might have noticed the subtle animations running along the margins. Those aren’t just random patterns—they’re cellular automata, simple rule-based systems that create surprisingly complex behavior.

What is a Cellular Automaton?

A cellular automaton is a grid of cells, where each cell can be in one of a finite number of states (typically “alive” or “dead”). The grid evolves over discrete time steps according to simple rules based on the states of neighboring cells.

Despite their simplicity, cellular automata can produce incredibly rich and complex patterns, making them a favorite subject of study in mathematics, computer science, and even philosophy.

Conway’s Game of Life

The most famous cellular automaton is Conway’s Game of Life, invented by mathematician John Conway in 1970. It follows just four rules:

1. Any live cell with fewer than 2 live neighbors dies (underpopulation)
2. Any live cell with 2 or 3 live neighbors survives
3. Any live cell with more than 3 live neighbors dies (overpopulation)
4. Any dead cell with exactly 3 live neighbors becomes alive (reproduction)

From these simple rules emerge complex behaviors: gliders that travel across the grid, oscillators that pulse in place, and even structures that can compute arbitrary functions.

Patterns You Can See

On my homepage, you can select different patterns:

• Gliders: Small patterns that move diagonally across the grid
• Pulsar: A period-3 oscillator that pulses in a beautiful symmetric pattern
• Pentadecathlon: A period-15 oscillator that stretches and contracts
• Spaceships: Larger patterns (LWSS) that travel across the grid

Elementary Cellular Automata & Rule 45

While Conway’s Game of Life operates in 2D, elementary cellular automata work in 1D. Famously studied by Stephen Wolfram, these automata have 256 possible rules numbered 0-255.

Rule 45 is particularly interesting because it produces complex, seemingly random behavior from a single starting cell. Starting with one cell at the top, it builds downward like a pyramid, creating intricate fractal-like patterns.

The rule works by looking at each cell and its two neighbors (3 cells = 8 possible combinations), then determining the next state based on a lookup table derived from the binary representation of 45.

Why I Love Them

Cellular automata represent something profound: complexity emerging from simplicity. They demonstrate that you don’t need complicated rules to create rich, interesting behavior—sometimes the simplest systems produce the most surprising results.

This idea has influenced my thinking about software engineering and AI systems. Often, the most elegant solutions come from finding the right simple primitives that compose into complex behavior.

Try It Yourself

Play with the patterns on my homepage! Use the dropdown to switch between different automata, and hit pause to freeze a moment in time. Watch how different initial conditions lead to vastly different outcomes.

If you want to dive deeper, I recommend:

• LifeWiki - An encyclopedia of Game of Life patterns
• Stephen Wolfram’s “A New Kind of Science” - A deep exploration of cellular automata
• Golly - A powerful cellular automata simulator

---

The animations on this site are built with vanilla JavaScript and HTML Canvas. They’re designed to be lightweight and pause when you’re not looking at the page.