Euclidean Go: A Geometry-Blind Go Engine That Runs on Any Euclidean Tiling

Introducing the Euclidean Go project—a revolutionary Go engine with a geometry-blind design using graph neural networks, capable of running on square, hexagonal, triangular, Archimedean tilings, and even non-periodic Penrose tilings without retraining. Developed by Alexandre Dufour-Richard, the project was released on GitHub in June 2026.

Go has been confined to the 19×19 square board for thousands of years. Euclidean Go raises a core question: Is Go inherently about geometric shapes or graph structural relationships? The answer is the latter—Go is essentially a graph game (stones as nodes, connections as edges, rules independent of grid shape).

Key technologies include:

1. Rule Engine: Processes stone removal, suicide prohibition, superko (Tromp-Taylor rules + Zobrist hashing), and area scoring based on graph structures;
2. MCTS: AlphaZero-style PUCT search (implemented in Python/C++), expanded on graph structures;
3. Neural Network: Geometry-blind design that only operates on BoardGraph, using Laplacian eigenvector position encoding (no coordinate information), with features including game state, node degree, boundary distance, etc.;
4. Tiling Compiler: Converts 11 types of Euclidean uniform tilings, rectangles, and Penrose tilings into a unified graph representation;
5. Training: Pure self-play (no human game records), with mixed tiling training data.

Experiments show:

• Square board: Reaches amateur-level performance;
• Non-square tilings: The mixed-training network outperforms expert networks trained only on square boards;
• Zero-shot transfer: Can reason on unseen tilings (e.g., some Archimedean tilings, larger Penrose regions) without fine-tuning, proving it learns tiling-agnostic concepts rather than grid memorization.

1. Python Server: Full functionality (territory estimation), requires Python/PyTorch, command: uv run python scripts/play.py;
2. Pure Web App: Offline available, open webapp/tilinggo.html;
3. Native macOS App: High performance (C++/Accelerate optimized, ~0.3 seconds per move, adapted for Apple Silicon), build command: python scripts/build_native.py.

Academic Value: A testbed for deep learning generalization ability, exploring graph neural networks in strategic games, zero-shot transfer, geometric invariance learning, etc.; Open Source: Apache-2.0 license, includes self-play weights, providing a platform for researchers.

Euclidean Go represents a new direction in AI game research—treating the board as a malleable graph structure rather than fixed geometry to achieve true generalization. Author's quote: "The board is data, not architecture." Project links: GitHub (https://github.com/vonduffen/euclidean-go), Online Demo (https://vonduffen.github.io/euclidean-go/).