I'm trying to figure out how the "fat cross" figures out how to expand. There are a few obvious parts - the outer boundaries are always 3 squares wide, for example. But I can't figure out how it's working the rest of the squares. It's most apparent at Legendary city size.

As you can see in this picture, the edges are pretty staggered, making it suggest that they are going with a 'round' edge system. But if they are, I can't figure out how they are determining whether a square should or should not be within the city boundaries.

Anyone have an idea? At first I went with a simple 'circle' system, where if your boundary was, say, 4 (that is, your borders extend 4 squares along x, y, -x, -y), then it would only encompass squares that were sqrt(x^2 + y^2) <= 4. Unfortunately, this doesn't seem to be the case. At 4 squares, the border encompasses the square +3, +3 (which is approximately 4.24).

So at this point I can't figure out how they are doing it.

Bh

As you can see in this picture, the edges are pretty staggered, making it suggest that they are going with a 'round' edge system. But if they are, I can't figure out how they are determining whether a square should or should not be within the city boundaries.

Anyone have an idea? At first I went with a simple 'circle' system, where if your boundary was, say, 4 (that is, your borders extend 4 squares along x, y, -x, -y), then it would only encompass squares that were sqrt(x^2 + y^2) <= 4. Unfortunately, this doesn't seem to be the case. At 4 squares, the border encompasses the square +3, +3 (which is approximately 4.24).

So at this point I can't figure out how they are doing it.

Bh

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