wendy wrote:Not really. If you were living at the scale where a house-block is the size of a cell of 4,5, then eighty blocks away is enough for one to get lost in a big way (like there are 100,000,000 blocks give or take some, in that range). It would be much worse than getting lost in a foreign city, for example.
For example, if you were to put the earth in the size of one of these cells, at 4000 miles diam, the whole universe fits inside the size of the sun of 864000 kms., and that's only something like 432 blocks away.
That makes me want to see a videogame implemented in such a city...
Hmm, so let's see. If the streets had consistency of, say, {oo,3} there WOULD be a simple way to mark the crossroads: you could mark the origin as 0, three branches as A,B,C and then give labels to further crossroads based on whether you go left or right to get there (like ALLR for "go through A branch, then go left twice and right once"). Since there are infinitygons, any combination would be unique. And computing distance (at least taxicab distance) between any two points is then very simple: if they start with same string, cut it off maximally and add the number of remaining symbols, if they don't start with same string, just add the symbols.
Which leads me to believe that the finitegonal tesselations might be doable by expressing them as a suitable group. A (6,8,10) tesselation, for example, has three kinds of edges, so directions can be given as "traverse a-edge (6-8), b-edge (6-10) or c-edge (8-10)", with simplifying rules stating that a^2, b^2, c^2, (ab)^3, (ac)^4 and (ad)^5 are all identities (more rules would be probably needed). Ideally, you'd end with 1-1 mapping of points and valid strings forr a given tesselation. Then, you could simply post waystones pointing to neighbouring vertices (with their labels) and you wouldn't get lost...