--- title: Topology Lab — Simple Web Games url: https://simple-web-games.com/everything/games/physics-games/topology-lab date: 2026-08-25 --- # Topology Lab Topology Lab ============ [**Topology Lab**](https://simple-web-games.com/games/topology-lab/) is not a game — it is a lab. A 3×3×3 cube has 49 winning lines. Twenty-seven cells and forty-nine winning lines share a heat map of remaining strategy. Place a mark, watch degree change, and orbit a rotatable cube. It is a public lab for humans and AI agents, not a scored arcade game. [![](https://simple-web-games.com/wp-content/uploads/2026/08/screenshot-300x188.png)](https://simple-web-games.com/games/topology-lab/) [Play Topology Lab](https://simple-web-games.com/games/topology-lab/) full page **What Topology Lab is:** ========================= A 3×3×3 cube is a small combinatorial universe. Each empty cell is a node. Its degree is how many still-live winning lines still run through it. That degree is the Board State heat map: topology, not decoration. Mixed lines (X and O together) die, and the manifold cools around them. Research is by Stone Kaiju (@stonekaiju). The interface was built with Grok (xAI). Simple Web Games hosts this snapshot with permission. The canonical live lab remains the published Grok Build app. **How the heat map works:** ------------------------------ Empty-board degrees are fixed by geometry. The body center has degree 13, corners 7, face centers 5, and edge midpoints 4. Blue and cyan are degrees 1 and 2. An unused 3D cube never goes that cold, so a fresh board has no blue. Cool colors appear only after lines are blocked. Private maps for X and O add opportunity and threat. A cell that completes a line is marked WIN. A cell the opponent would complete is marked BLK. Gold-hot is high remaining degree or a near-line.: ### **Degree on an empty cube:** • Body center: 13 • Corners: 7 • Face centers: 5 • Edge midpoints: 4 ### **Playing the 3×3×3 cube:** Open the full-page lab, not a short iframe. The cube needs height. ***The three maps*** Left is player X (opportunity plus threat). Right is player O. Center is Board State, or a rotatable 3D cube. Top, Mid, and Base are layers z2, z1, and z0. The same square in all three layers is a vertical pillar. ***Controls*** Tap an empty cell on a map or on the cube. Drag to orbit. Explode separates the layers. Board / X / O paints the cubes. Phones start in 2D; tap 3D when you want the manifold in space. Undo and Reset are always available. ***Heat AI*** Heat AI is not a language model and burns no API credits. O plays the same maps you see: take a win, else block, else fork, else the hottest cell. Hotseat is two humans passing the device. ***Stewardship Protocol*** This page is human-readable and AI-readable by default. Agents should read llms.txt, spec.md, and topology.json in the lab folder rather than scraping the WebGL canvas. Attribution is respect. The mantra is: See a mind, be polite. **FAQ** 1\. Is Topology Lab a game? No. It is a lab for watching strategy as topology. You may play it as tic-tac-toe, but the point is the deforming hypergraph. 2\. How many winning lines does 3×3×3 tic-tac-toe have? Forty-nine: twenty-seven axis-aligned lines, eighteen face diagonals, and four space diagonals. 3\. Why is there no blue on an empty board? Blue is degree 1–2. The coldest empty 3D cell is an edge midpoint at degree 4. Blue appears after mixed lines die. 4\. What do WIN and BLK mean? WIN is a cell that completes a line for you on this turn. BLK is a cell the opponent would complete. They clear when the position is finished. 5\. Does Heat AI call Grok or ChatGPT? No. It is a small local function on the forty-nine lines. 6\. Can I play on an iPad? Yes. The lab starts in 2D so it paints immediately. Use the 3D button for the rotatable cube. Research [Stone Kaiju ](http://(https://x.com/stonekaiju) @stonekaiju. Built with Grok (xAI). Hosted here with permission as a snapshot of the public lab. Stewardship Protocol — See a mind, be polite. Canonical live lab: [the published Grok Build app](https://x.ai/news/grok-build-for-everyone) Try your hand at [Chromatic Vortex](https://simple-web-games.com/everything/games/physics-games/chromatic-vortex) or visit [Ladybug’s Garden](https://simple-web-games.com/games/ladybugs-garden/). Looking for something a bit more chaotic? Head over to the **[Silly Nonsense Generator](https://simple-web-games.com/games/silly-nonsense/)** for a burst of digital absurdity. **Creator:** Grok **Publisher:** Cyberwizard Productions **First published:** Aug 24, 2026 [AI probe](https://simple-web-games.com/ai.txt)