How to Play

📜 Understanding the Rules

Conway's Game of Life is a "zero-player game"—once you set up an initial pattern, it evolves on its own. Each cell on the grid is either alive (filled) or dead (empty), and every generation, cells live or die based on their neighbors.

◆ Math Arcade: LIFE Forge

LIFE Forge turns the mathematics into a hands-on puzzle game. Open Math Arcade from the header or mobile controls, choose a challenge, and draw a witness on the 9×9 forge. Every result is checked under exact B3/S23 infinite-plane evolution—never by animation speed, population-only guesses, or device performance.

1. Build a Conjecture

   Try stability, exact period 2, spaceship motion, a one-generation parent of the block, or maximum-density 4×4 packing. Drag to paint, tap to toggle, or use arrow keys plus Space.

2. Run the Exact Proof

   The verifier compares complete cell states. Oscillators must return at their fundamental period; spaceships must repeat the exact shape with consistent integer displacement through another full cycle.

3. Understand a Miss

   A failed attempt explains what the engine actually observed and gives a next action. Hints are optional, retries are unlimited, and time never changes the score.

4. Preserve and Improve

   Bronze, Silver, and Gold use deterministic cell-count or density thresholds. Best proofs are revalidated from their stored RLE on this device, and the certificate links to the relevant LifeWiki concept.

🎮 Getting Started

1. Draw Your Pattern

   Click on cells to toggle them alive or dead. Use the Draw tool for continuous drawing, or Erase to remove cells. You can also use the Randomize button for a quick start.

2. Use the Pattern Library

   Select from 15+ classic patterns in the sidebar. Click a pattern to select it, then click on the grid to place it. Use Q/E or the rotation buttons to rotate patterns before placing.

3. Start the Simulation

   Press the large Play button or hit Space. Watch as your pattern evolves! Adjust the speed slider to go faster or slower.

4. Explore & Experiment

   Try different patterns, enable cell aging to see how long cells survive, or turn on trails to track cell movement. Zoom in/out with scroll or the zoom buttons.

5. Compete on the Leaderboard

   Eligible Classic runs can submit after an exactly detected static pattern, oscillator, or extinction; the stochastic Evolution Sandbox ends automatically only on extinction. Custom rules and finite Evolution Trials are excluded. Community Runs are an informal comparison of disclosed setups, not identical-seed competition.

⌨️ Keyboard Shortcuts

Master these shortcuts to navigate like a pro:

🧬 Using Evolution Mode

Evolution Mode gives each cell its own inherited birth and survival phenotype. The rule badge shows the most populous expressed lineage; it is telemetry, not one global ruleset that the game rewrites.

1. Enable Evolution Mode

   Toggle the Evolution switch in the control panel. You'll see new stats appear: Pressure, Mutations, and Fitness.

2. Prepare the Starting Board

   Draw, place active patterns, or randomize before launch. Ranked Balanced and Sparse starters replace the board with a canonical 50×50 torus, making difficulty identical across screen sizes. My Board preserves your exact nonempty setup as unranked Practice.

3. Choose Sandbox or a Trial

   Sandbox is open-ended. Endurance holds at least 300 cells after generation 25, finishes 250 with at least 500, and earns a score of at least 600. Diversity needs a 30-generation streak with effective diversity at least 3 and no phenotype above 65%. Adaptation survives 300 and averages at least 20 fitness over the final 50 generations. Stronger sustained results earn Silver or Gold.

4. Choose the Mutation Protocol

   Pick Preserve (0.5%), Explore (2%), or Shock (10%) for the opening phase, then choose again at generations 80 and 160 in Endurance or 100 and 200 in the other Trials. The newborn's inherited mutability can add up to 2 percentage points. Every choice is captured in the receipt.

5. Read Births and Lineages

   The most common neighboring birth-rule coalition authorizes an empty site. Tied coalitions combine their allowed counts without scan-order bias. Only neighbors whose own expressed birth rule allowed the actual count can become vigor-weighted genetic parents.

6. Finish, Retry, or Keep Exploring

   A Trial loses immediately on extinction, stops exactly once at its terminal result, and offers Retry Same Seed, New Seed, or Reset to Sandbox. Ranked guided runs save the best local Bronze, Silver, or Gold medal; My Board Practice never changes progression. No Trial submits to Community Runs.

⚙️ Custom Rules Editor

Want to explore beyond Conway's classic rules? The Custom Rules Editor lets you create your own Life-like automata!

How It Works

Outer-totalistic Life-like automata use B/S notation: Birth conditions and Survival conditions based on neighbor counts (0-8).

• Birth (B): How many neighbors cause a dead cell to become alive
• Survive (S): How many neighbors let a living cell survive

For example:

• B3/S23 — Conway's Life: birth on 3, survive on 2-3
• B36/S23 — HighLife: adds replicators!
• B3/S12345 — Maze: creates corridors

Exact Hensel Rules and RLE

Isotropic Hensel letters distinguish neighbor arrangements that have the same count. Export Board (RLE) writes the trimmed live-cell bitmap and the exact active outer-totalistic or Hensel notation. Importing the RLE restores every partial Hensel class exactly and selects the bitmap for placement; it does not silently expand a partial B3 class into all B3 neighborhoods.

🔒 Locked Run Configuration

The first Play or Step fixes the run-defining setup: Classic or Evolution mode, board size, global rule, edge wrapping, mutation rate, pattern placement, and randomization. Desktop controls, mobile controls, and keyboard shortcuts all respect the same lock; rule/RLE import is also refused during an active run. Press Clear to configure a new attempt. Speed, grid, trails, aging colors, pan, and zoom remain available because they do not change the simulated outcome.

🎛️ Other Settings

Wrap Edges (Toroidal)

When enabled, opposite edges are adjacent, making the finite board a torus. Disable wrapping for dead space beyond the board boundary. Pattern Discovery uses its own growable open-plane verifier regardless of this play-board setting.

Show Cell Trails

Enables fading trails that show where cells recently died. Useful for visualizing spaceship movement and oscillator patterns.

Cell Aging Colors

Colors cells based on how many generations they've survived. New cells are bright green; ancient survivors fade to pale green. Great for identifying stable structures.

🔬 Pattern Discovery Mode

Pattern Discovery searches B3/S23 soups with 13 configurable generators. Its classifier verifies behavior separately from catalog novelty.

1. Launch Discovery Mode

   Press D or click the Discover button in the control panel. A floating panel will appear showing real-time search progress.

2. Watch the Search Progress

   Choose sequential, random, focused, or weighted cycling. Weighted mode uses UCB1: every enabled strategy is tried, then finds per analyzed soup are balanced against an exploration bonus. Productive strategies get attention without starving less-tested ones.

3. Trust Verified Behavior, Not an Edge Artifact

   Candidates run on a growable dead-border sandbox that models the open plane and never wraps opposite edges. Exact repeating states verify oscillator periods; consistent integer displacement verifies spaceships. If the safety ceiling is reached, the result stays unresolved.

4. Interpret Catalog Status Carefully

   Known, not found, lookup unavailable, and uncheckable are different. An encodable still life, oscillator, or spaceship not found by Catagolue is only an uncatalogued candidate. Transient methuselah and diehard seeds do not have the required object code, so they are marked uncheckable and need a manual census search—never an automatic novelty claim.

5. Place or Export a Discovery

   Select a session result, place it on the main board, or export its RLE. Recheck any novelty candidate independently before publishing a claim.

🔗 Sharing Your Creations

Created an interesting pattern? Share it with friends!

1. Open Share Dialog

   Click the Share button in the header (the icon with connected dots).

2. Copy the URL

   An anonymous short URL is retained for one year and preserves Classic live-cell positions, board size, outer-totalistic B/S rule, and edge wrapping. Evolution genes and exact isotropic/Hensel classes are not included; the Share dialog labels that limitation. Export Board RLE for a permanent copy or when exact Hensel rule transfer matters.

3. Send to Anyone

   Anyone who opens the link will see your exact pattern, ready to run!