LibraryOf2048

Overview

LibraryOf2048 is a Rust-based application that catalogs and indexes all ~117 quintillion possible board states of the classic 2048 game. Inspired by Jonathan Basile’s Library of Babel, this project provides a deterministic, navigable archive of all valid 4×4 tile configurations using a two-part keying system that enables efficient enumeration and lookup. The project includes a GUI interface, and serves as a platform for further research into solving the stochastic dynamics of 2048, a PSPACE-complete challenge.

Core Concepts

The enumeration system is based on a dual-ID system and t-value, forming an efficient data triplet that distinguishes each individual board:

1. T-Value (Tile Count)

• Represents how many tiles are on the board.
• Valid t values range from 2 to 16.
• Boards with t=0 or t=1 are not used, as the game always starts with 2 tiles and never decreases tile count below that value.

2. Global ID (Tile Placement)

• Encodes the positions of tiles on the 4×4 board.
• For a given t, the global ID is a linear index across all $\binom{16}{t} - 17$ permutations of tile placements (17 is the number of states t=0 and t=1 account for).
• Ranges from 1 to 65519, accounting for all valid tile-position combinations.

3. Local ID (Tile Values)

• Encodes the values of each tile in a board configuration.
• Uses base-11 notation to represent tile values ([2, 4, ..., 2048]), mapped as digits representing powers of 2: ([1, 2, ..., A]).
• The length of the local ID equals the t value; each digit corresponds to a tile's value, applied in left-to-right order on the board as dictated by the Global ID.

Example:

If t=2, Global ID = 119, and Local ID = AA:

• The board has two tiles.
• Their positions are derived from Global ID 119.
• Each tile is a 1024-tile (2^10 = 1024).

This systematic encoding allows precise generation, lookup, and traversal of the 2048 board space—over 1.17e20 (~117 quintillion) possible configurations.

Features

• 📚 Full Enumeration of all 2048-valid board states
• 🔍 Lookup by ID — decode or explore by Global + Local IDs
• 🖼️ GUI Interface — built with egui, powered by Rust
• 🧠 Research-Oriented — supports investigation into PSPACE-level complexity of 2048

Installation

Prerequisites

• Rust toolchain (stable)

Build

git clone https://github.com/jwm-dev/LibraryOf2048.git
cd LibraryOf2048
cargo build --release

Technical Details

• Language: Rust
• GUI: egui
• Encoding: Base-11 local ID, combinatorial indexing of placements
• Optimization: Indexed retrieval, fast computation, zero-copy board generation
• Scope: ~1.17×10²⁰ valid board states

Inspiration

This project is inspired by Jonathan Basile's Library of Babel, which exhaustively indexes all possible combinations of characters in the Latin alphabet. LibraryOf2048 follows a similar philosophical and technical arc — providing total determinism and structure to an otherwise intractable combinatorial space.

Future Work

• Solve the stochastic, classic variant of 2048 through AI or formal methods
• Visual analytics for tile distributions and win conditions
• WebAssembly interface for browser-based board browsing

Related Projects

• BoardViewer_2048
  Command-line interface for browsing protoboard states by ID.
  → 2048 Board Viewer CLI

• ProtoboardEnum_2048
  Generates and indexes all 65,519 valid protoboard configurations — binary tile presence patterns on a 4×4 grid, used as structural templates for full 2048 board states.
  → 2048 Protoboard Enumeration

License

MIT License. See LICENSE file.

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LibraryOf2048: not just a game, but a universe of structured possibility.