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This commit is purely frivolous even by Puzzles standards, in that it's totally unrelated to any actual puzzle. But I know at least one person has already used the 'hat-test' tool in this code base to generate a patch of hat tiling for decorative purposes, so it's useful in its own right. Also, now that I've worked out _how_ to do this, it's a shame not to keep the code. Of course, any tiling of the plane _can_ be four-coloured, just by the Four Colour Theorem. But for a tiling with structure it's nicer if the colouring is related to the structure in some way. And there's a reasonably nice explicit construction that does just that: the paper introducing the tiling observes that if each reflected hat is fused with a particular one of its neighbours, the resulting tiling is graph-theoretically equivalent to a tiling of the plane by hexagons. And _that_ tiling can be three-coloured, in a unique way up to colour choices. This induces a four-colouring of the hat tiling in which the reflected hats have a colour to themselves, and everything else is coloured the same as its corresponding hexagon in the three-colouring. Actually implementing this turns out not to be too difficult using my coordinate system. I hand-wrote tables giving a patch of colouring for each of the four kitemaps; then, whenever two kitemaps meet, you can determine how the colours map to each other by looking at the overlapping tiles. So I can have hat-test work out the colour of each tile as it goes. So hat-test now supports a '--fourcolour' option to apply this colouring to the output tiling.
This is the README accompanying the source code to Simon Tatham's puzzle collection. The collection's web site is at <https://www.chiark.greenend.org.uk/~sgtatham/puzzles/>. The puzzle collection is built using CMake <https://cmake.org/>. To compile in the simplest way (on any of Linux, Windows or Mac), run these commands in the source directory: cmake . cmake --build . The manual is provided in Windows Help format for the Windows build; in text format for anyone who needs it; and in HTML for the Mac OS X application and for the web site. It is generated from a Halibut source file (puzzles.but), which is the preferred form for modification. To generate the manual in other formats, rebuild it, or learn about Halibut, visit the Halibut website at <https://www.chiark.greenend.org.uk/~sgtatham/halibut/>.