Four Color Map
The four color theorem says any flat map can be colored with just four colors so neighbours always differ — a claim so slippery it resisted proof for 124 years and finally needed a computer. Here a random map is generated and you color it yourself: click a region to cycle colors, conflicts flash red, and a counter tracks colors used. Stuck? The solver colors it with four using backtracking — as the theorem promises it always can.
Runs 100% in your browser — simulations are computed locally on your device.
Read the full guide to this tool
Notes
- Proved in 1976 by Appel and Haken — the first major theorem proved with a computer.
- Three colors are not enough: four mutually touching regions already need four.
- On a torus you need up to seven colors — the topology of the surface decides.
- Runs 100% in your browser — simulations are computed locally on your device.
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