Well, that's better, I guess. You can tell where your influence is--but wait, why isn't that fire shard in my influence? It's only two tiles away. Oh, but it's still using the Euclidean distance formula to set the powers. Well, that's lame, and it makes it look lame too. No one is going to look at this and say, "Oh, it's calculating the Euclidean distance from the city hub." They're going to count the tiles.
So I made it not check the Euclidean distance and just check everything in the bounding rect with the source at its center and a radius of 2.
Meh, I much prefer using the Euclidean distance than the min(|,|y|) distance (like you used in the last screenshot). The problem with the using the minimum of the x- and y-distances is that it creates square instead of circular ZoC, which is much too blocky for my taste.
Anyway, if you use Euclidean distance, and you want to avoid the ugly cross you got in second-to-last screenshot, you should always add one-half to your distances, instead of using integers distance only. For instance, by using a radius of 2.5, you will get the "fat cross" that is well known by any Civilization 1,2,3,4 player. (Note: using radius + 1/2 is equivalent to rounding the distance between tiles, instead of taking the integer part.)