About LIFE

🌱 What is Conway's Game of Life?

Conway's Game of Life is a cellular automaton devised by British mathematician John Horton Conway in 1970. Despite being called a "game," it requires no players—you simply set an initial configuration and watch it evolve according to four elegantly simple rules.

The Game of Life is a prime example of emergent complexity—how intricate, unpredictable behavior can arise from simple rules. It has fascinated mathematicians, computer scientists, and philosophers for over 50 years, demonstrating concepts fundamental to artificial life, complexity theory, and even the nature of computation itself (it's Turing complete!).

The Four Rules

• Underpopulation: A living cell with fewer than 2 neighbors dies from loneliness
• Survival: A living cell with 2 or 3 neighbors lives on to the next generation
• Overpopulation: A living cell with more than 3 neighbors dies from overcrowding
• Reproduction: A dead cell with exactly 3 neighbors springs to life

🧬 What Makes This Simulator Special?

This isn't just another Game of Life implementation. We've created the most feature-rich, visually stunning, and scientifically interesting cellular automaton simulator available online—completely free and running entirely in your browser.

🔬 Evolution Mode Explained

Our unique Evolution Mode takes the Game of Life to an entirely new level. Instead of fixed rules (B3/S23), the rules themselves become subject to mutation and natural selection.

The system evaluates each ruleset using a fitness function that considers population density, stability, and dynamic behavior. When certain conditions are met, the rules mutate—adding or removing birth/survival conditions. Poor mutations that cause extinction or explosive growth are automatically reverted.

This creates a meta-evolution where you can watch the discovery of entirely new cellular automata in real-time. You might see your simulation evolve from Conway's Life (B3/S23) to HighLife (B36/S23) to completely novel rulesets that sustain interesting behavior.

🔬 Pattern Discovery Engine

Our Pattern Discovery Engine uses advanced mathematical techniques to automatically search for new life patterns—oscillators, spaceships, still lifes, and more. Press D or click the Discover button to launch it.

Mathematical Foundations

The engine employs sophisticated algorithms from multiple mathematical domains:

• Genetic Algorithm: Evolves candidate patterns through selection, crossover, and mutation to breed increasingly interesting configurations
• D₈ Dihedral Group: Uses all 8 symmetry transformations (4 rotations × 2 reflections) to canonicalize patterns and prevent duplicate discoveries
• Brent's Cycle Detection: O(λ+μ) algorithm that detects oscillator periods, even for very long-period patterns (p3, p5, p15, p46, etc.)
• Shannon & Rényi Entropy: Measures structural complexity and information content of patterns
• Discrete Fourier Transform: Analyzes population dynamics to detect periodic behavior
• Autocorrelation Analysis: Finds repeating patterns in time series data for period estimation
• Lyapunov Exponent: Estimates sensitivity to initial conditions (chaos vs. stability)
• Kolmogorov Complexity: Approximated via compression to measure pattern simplicity
• Moran's I: Spatial autocorrelation measuring clustering in patterns

What It Discovers

• 🚀 Spaceships: Patterns that translate across the grid. The engine calculates velocity as a fraction of c (speed of light) and detects oblique and glide-symmetric ships
• 🔄 Oscillators: Patterns that repeat after n generations. Detects periods from 2 to 500+, with bonus scoring for rare prime periods
• 🪨 Still Lifes: Stable patterns that never change
• 🌟 Methuselahs: Small patterns with surprisingly long lifespans before stabilizing

Fitness Scoring

Each candidate pattern is scored using a multi-factor fitness function:

• Pattern type bonus (spaceships: +500, oscillators: +100, still lifes: +40)
• Logarithmic period scoring (longer periods = exponentially higher scores)
• Prime period bonus (period 3, 5, 7 oscillators are mathematically interesting)
• Entropy-based structural complexity scoring
• Novelty bonus for previously unseen canonical forms
• Spaceship speed and direction bonuses (oblique ships are extremely rare)

🏅 The Leaderboard Challenge

How long can your simulation run before reaching stability? The leaderboard tracks the number of generations before your pattern becomes static, extinct, or enters a repeating cycle.

There are two separate leaderboards:

• Classic Mode: Standard Conway's rules (B3/S23)—pure skill in initial pattern design
• Evolution Mode: Adaptive rules—can you find initial conditions that evolve into long-running rulesets?

When your simulation stabilizes, enter your initials arcade-style and see where you rank globally!

🚀 Built By

📖 Learn More

Interested in cellular automata and the Game of Life? Here are some concepts worth exploring:

• Turing Completeness: The Game of Life can simulate any computer program
• Garden of Eden: Patterns that cannot arise from any predecessor
• Methuselahs: Small patterns that take a very long time to stabilize
• Replicators: Patterns that create copies of themselves
• Life-like Automata: Other rulesets (like HighLife, Day & Night) with similar properties