Wednesday, September 28, 2022

Fun with Topology, Down in the Mystic Forest

("moon's haunted" voice):  rectangles arranged in brick pattern topologically isomorphic to hex grid.

what?

*screenshotting somerset art assets and getting onto photoshop to hack together a rough .png file* rectangles arranged in brick pattern topologically isomorphic to hex grid.


So I guess it never stopped bothering me that the roads/bridges mechanic in Somerset was a little too complicated and graphically confusing- in the playtesting group I was in in college we were always forgetting that there were certain ways that movement was limited. I always thought, maybe this would be better with squares instead of hexes? but then it wasn't complex enough, and there was too much blocked off to boot, with 1/4 of the edges untraversable bridgeless rather than 1/6.

Discovering that squares/rectangles tiled in an offset grid is topologically identical to tiled hexagons reminded me of this conundrum, and got me thinking again. If the squares were arranged in bricks, with one corner each cordoned off instead of one edge? Maybe not topologically indistinguishable from prior prototypes' regular hexagons with one side inaccessible (it's possible to have as much as 5/6 of the edgeage blocked off under this model, [edit: come to think of it it's possible to have 6/6 blocked off under the hexes]) but imho that makes it functionally better, providing hopefully the perfect balance of navigational affordances and meaningful need to circumnavigate/ bridgebuild. Maybe there's a way to do functionally the same thing with hexes, I don't know [edit: 1 full hex side, plus 1/2 a side? but that still allows 100% of a tile to be blocked off mathematically, as established in the earlier edit, whereas that's literally impossible with the square thing, so.] Certainly a lot easier to read the board this way with squares.