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This uses a tile shape very similar to the hat, but the tiling _structure_ is totally changed so that there aren't any reflected copies of the tile. I'm not sure how much difference this makes to gameplay: the two tilings are very similar for Loopy purposes. But the code was fun to write, and I think the Spectre shape is noticeably prettier, so I'm adding this to the collection anyway. The test programs also generate a pile of SVG images used in the companion article on my website.
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/>.