[Singularity24601]

Wraparound maps solve the strategic serendipity of map borders, but I dislike them because I find them hard to visualize. On a spherical world, if you head far enough east, you reach the west, but you don't reach south if you head far enough north - that would only be true if you were on a torus (a doughnut). On a sphere, if you're on the eastern hemisphere and head far enough north, you reach the north side of the western hemisphere, now heading south. I propose two methods of simulating spherical worlds:

1) Modified tesselation
I believe it should be possible to achieve a closer approximation to a sphere by rotating each "row" of iterations by 180 degrees (ie, vertically and horizontally flipping). I have attached diagrams to demonstrate:
Image 1: Torus tesselation
Image 2: Incorrect sphere tesselation
Image 3: Correct sphere tesselation

2) Cylindrical projection
Simply neighbour the eastern and western edges (with or without tesselation), provided 2 conditions are met:
- All provinces of the northernmost and southernmost latitudes must be neighbours with each other (equivalent to dividing arctica/antarctica like a pie).
- The number of provinces per latitude must be a maximum in the equatorial latitude, decreasing roughly trigonometrically to minimums at the northernmost and southernmost latitudes (eg, 1-3).

To achieve these conditions will result in some distortion:
- As one approaches the polar extremes, the shape of the provinces are preserved, but the area of the provinces become progressively larger (Mercator projection).
- As one approaches the polar extremes, the area of the provinces are preserved, but the shape of the provinces become progressively flatter (eg, Gall-Peters projection).
- A compromise between the two extremes (eg, equidistant cylindrical projection).