Topoboardgame

Topological Board Game

Same Core Rules. Different Spaces. New Strategy.

TopologicalBoardgame is an interactive platform for classic and physics-inspired board games on changing spaces.

For players, it transforms familiar rules into new strategic worlds: easy to enter, surprising to play, and deep enough to challenge serious competitors.

For researchers, it becomes a visual and playable laboratory for studying how information, locality, symmetry, competition, and physical behavior change when the underlying space changes.

A move is never just a move here. It is a test of the space itself.

You-Xun Zhang youxunzhangjim@gmail.com

Choose entry

Two ways into Topoboard

Use the same visual style and controls, then enter either a player-friendly arrangement or a research workspace.

Players Simple play, clear rules, local robots, online rooms, Life World play, and game guides. Board Worlds Choose Chess, Go, Reversi, or Chinese Checkers-style Jump. Life World Play Play cellular automata and species challenges with beginner controls.

Researchers Reproducible Labs workflows for topology, observables, batch runs, regime maps, and same-rule comparisons. Same Rule, Different Space Compare one local rule across torus, cylinder, Mobius, and other topologies. Experiment Builder Build seed-stored batches, exports, and topology comparisons for research.

2D Games embedded in 2D space 2D Chess Chess with selectable boundaries 2D Go Go with selectable topological boundaries 2D Reversi Reversi with selectable boundaries 2D Jump Step moves and chain jumps on standard/topological boards

3D Games embedded in 3D space 3D Chess Chess on interactive topological boards 3D Go Go on rotatable lattice boards 3D Reversi Reversi on rotatable lattice boards 3D Jump Chain jumps through volumes, shells, and wrapped spaces

4D Games embedded in 4D space 4D Go Go on 4D slice boards 4D Reversi Reversi on 4D slice boards 4D Jump Projected higher-dimensional chain-jump races

2+1D Games embedded in 2+1D spacetime 2+1D ChessChess-like movement with Time schedule and optional Age 2+1D GoPlace stones with Time schedule, Go-only Time period, optional Age, and optional noise 2+1D ReversiFlip lines with Time schedule, optional Age, and optional noise 2+1D JumpChain-jump races with Time schedule and target timing

3+1D Games embedded in 3+1D spacetime 3+1D ChessVolume chess timing with Time schedule and optional Age 3+1D GoPlace stones through layers with Time schedule, Go-only Time period, optional Age, and optional noise 3+1D Reversi3D line flipping with Time schedule and optional Age 3+1D JumpVolume jumps with Time schedule and explicit target zones

Strategy & Systems Labs (Developing) Choose a playable lab world to explore new rules, hidden structures, and strategic patterns. Open Info to learn what the system represents, how it changes the game, and what you can observe through play.

Spin & Phase Lab (Developing)

Black / white: Spin up/down or phase A/B.
Objects: Local spins, domains, droplets, and interfaces.
Goal: Order, coarsen, stabilize, or compare topology-driven domain walls.
Observables: Energy, magnetization, wall length, domain count, area fractions.
Recommended users: Players learning phase competition and researchers testing topology effects.

Info

Start here for phase-ordering play: Ising spins, two-phase growth, and cluster fields share local graph rules so topology changes which domains survive.

Domain Wall Thermal Spin Topology Compare

Quantum Information Lab (Developing)

Black / white: Positive/negative stabilizer or Pauli-frame signs.
Objects: Pauli labels, ancilla sites, stabilizer checks, and logical sectors.
Goal: Recover errors or benchmark Clifford/Pauli dynamics.
Observables: Syndrome weight, logical sector, measurement errors, recovery status.
Recommended users: Quantum information learners, QEC toy-model users, and stabilizer researchers.

Info

Use this lab for Pauli-frame and stabilizer recovery: make local corrections, measure syndromes, and check whether the logical sector stays correct.

Pauli Correction Stabilizer Check Clifford Toy

Anyon & Topological Memory Lab (Developing)

Black / white: Particle owners, charge signs, or competing anyon sectors.
Objects: Anyons, worldlines, fusion channels, gauge loops, and memory strings.
Goal: Create, braid, fuse, unbraid, or preserve topological memory.
Observables: Fusion result, braid parity, charge, Wilson sector, memory alive.
Recommended users: Players exploring particle strategy and researchers testing topological memory.

Info

Use this lab for anyons and topological memory: create particles, braid or unbraid worldlines, fuse charges, and check whether memory remains in the vacuum or target sector.

Toric Anyons Braid Memory Energy Excite

CFT / Field Theory Lab (Developing)

Black / white: Source sign, domain sign, or player control of insertions.
Objects: Primary fields, OPE intervals, conformal blocks, and Virasoro actions.
Goal: Measure correlations, select OPE channels, and test anomaly/stress response.
Observables: Primary counts, cross-ratio, block weights, entropy, anomaly events.
Recommended users: CFT learners, mathematical-physics players, and field-theory researchers.

Info

Use this lab for discrete CFT graph models: insert primary fields, update OPE channels, and measure correlations, conformal blocks, entropy, and anomaly response.

Four-Sigma Correlator Virasoro Toy

Advanced Algebra Sandbox (Developing)

Black / white: Defined by the selected engine and physical problem.
Objects: Stones, particles, Pauli frames, primary fields, gauge edges, spins, or domains.
Goal: Expose the full research workbench without hiding internal controls.
Observables: Every engine export, history trace, physical answer, and raw diagnostic.
Recommended users: Advanced users who want direct access to the full engine and option set.

Info

Open the full engine controls and raw exports for advanced comparisons between modes, topologies, lattices, and physical problems.

Open Sandbox

Life & Evolution Worlds Choose the neighborhood rule first; choose geometry inside the Life page.

Pick one of three Life rule families below, then choose the board space, lattice, noise, age, species, and challenge settings inside the Life interface.

Info

Zero-player, one-player, two-player, and research modes for cellular automata, ecology, topology, complex systems, and AI experiments.

Moore Neighborhood Mode Von Neumann Neighborhood Mode Lattice Nearest-Neighbor Mode