I am a fan of civilization-style games, yet one way in which I am dissatisfied is how the maps are made. They are grids of squares wrapped around a cylinder, not including the top and bottom in any way. Personally, I am very unsatisfied with this incomplete, inaccurate, and boring layout.
For a good long time, I have sought a simple, yet effective means of having a specific number (in the hundreds or thousands or more) of close-to-circular tiles to be distributed evenly on a sphere. Obviously, the tiles wouldn't get any more circular than a collection of hexagons and pentagons (and maybe even some heptagons), but that's still a major improvement from a grid of squares, kite-shaped tiles, or triangles. The longstanding answer has been to only use numbers of tiles of the form 10*(x^2+xy+y^2)+2, then arrange them into a geodesic configuration. However, that always bothered me as the twelve pentagons were always smaller than all the hexagons, I couldn't get very exact locations of many of the tiles, and I could never get a number of tiles divisible by five. There was also how there are large gaps in what numbers work.
...but no matter. A number of days ago, I found another solution. ...and the funny thing is that nature (specifically plant biology) got there first.
Every two consecutive tiles are the golden ratio from each other in terms of longiture and right next to each other in terms of latitude.
First they go on the unit sphere.
z (height) = 2s/a-1, and theta (longitude) = a*(360 degrees or 2pi radians)*(golden ratio)
The golden ratio is (5^(1/2)+1)/2.
a is 1/2 less than the number of a specific tile on the globe.
s is the total number of tiles on the globe.
Latitude, distance from the polar axis, x value, and y value can be determined from those equations, but I'm a bit to lazy to explain how right now. xP
We then have a sphere covered in points that are of sufficiently even distribution (for me, at least). As an added bonus, the equation works for any number of tiles. However, for the next step, that number of tiles should hopefully be at least four unless for 3 tiles or less you don't mind either curved exceptions or infinitely large tiles.
My next step was to try to expand the points into tiles. Each tile is tangent with the sphere at the location of the point. So what happens is you have a plane for each point, and borders of adjacent tiles are where planes of close points intersect. The result is something similar to the image above, minus the terrain features.
The next step is to just resize the entire map, like multiplying it by the square root of the number of tiles. That way, when units, cities, terrain features, and other stuff are placed on them, they won't look too large on tiles of large worlds or too small on tiles of small worlds.
The final step, of course, is adding all the features.
The above map is a globe of 144 tiles, centered on the north pole, given a very basic terrain look, and made to look vaguely like Earth. I also decided to give shading to tiles faced farther away from the viewer, despite how the sun, the north pole, and the center of the Earth never line up.
If this isn't in the right category, please let me know so that I can change it before it gets erased from this site. o.o;
Edit: By the way, that dot in the middle of the map is the north pole, itself.