I'm not sure how what I said got misinterpreted, but apparently it did. I'm guessing its the merging comments. The borders around your cities are dependent primarily on the cities culture like I said. However, they also will merge and do odd things if other cities are nearby, and I don't think we know that algorithm yet.
I'm trying to find the screenshot I'm referring to, as I think that will make my point clearer, but I can't remember exactly where I saw it, as I've seen tons of screenshots in the past few days. Just imagine two cities with three empty squares between them. They each have a culture under 10, so their normal borders would be one square out. This would leave a single row open between them, with two seperate border areas. However, in the screenshot, the borders had shifted to include those three squares between the two cities that were not within one square of either city. Rather than having two 3x3 areas, they had merged into one 7x3 area.
I'm going to try and draw a text picture, so bear with me if it doesn't work.
This is what the culture rules would expect. C represents a city, - and | represent borders. x represents empty spaces so it's clearer.
<pre>
----- -----
|xxx|x|xxx|
|xCx|x|xCx|
|xxx|x|xxx|
----- -----
</pre>
However, this is what was shown.
<pre>
---------
|xxxxxxx|
|xCxxxCx|
|xxxxxxx|
---------
</pre>
.
I don't really see any other possible explanation for this type of observation.
More generally, the culture rule states where borders would be in the absence of any other influence, but when other of your cities are nearby, the borders can merge in ways we don't exactly understand yet, and obviously if you had two cities from different civilizations with high culture, their borders would conflict, and there have to be resolution rules for that. In the particular shot I saw, it appears possible that if a square is bordered on two sides (maybe it has to be opposite sides) by borders for the same civ, it will be claimed by that civ. Like I said, we don't know the exact rules for how borders merge or conflict yet.
I guess what I'm trying to say is that technically speaking, the culture rating of the city is not the only factor in determining borders, just the major one. There are other rules that apply. If you don't believe me, just think what happens when two civilizations build cities with just one square between them (okay if the culture levels are still low, since the new city won't be inside the border of the old city) and then the culture of both cities rises to over 1000. What happens to the borders? Obviously, both cities cannot claim all the territory within 4 squares of them.
Here's a visual representation of the above example. S represents a settler.
When the second city is going to be founded:
<pre>
-----
|xxx|
S|xCx|
|xxx|
-----
</pre>
.
Later on: (i.e. now what?) I'm guessing on how 4 square borders look, BTW. a is a square owned by the left city, b is a square owned by the right city, ? is who knows what.
<pre>
-------
--|aa?bb|--
|aaaa?bbbb|
-|aaaa?bbbb|-
|aaaaa?bbbbb|
|aaaaC?Cbbbb|
|aaaaa?bbbbb|
-|aaaa?bbbb|-
|aaaa?bbbb|
--|aa?bb|--
-------
</pre>
.
Hopefully I've helped clarify what I said. I'm getting worried now that I'm just confusing things. I guess what I'm trying to point out is that although a city's culture is critical in determining a civ's borders (and indeed, the civ's culture as a whole is possibly somewhat irrelevant, but then it may help resolve the scenario I proposed above), it's not the only factor. Other rules come into play when borders of different cities interact on the map.
(BTW, forgive the odd periods. The text seems to do funny things in my browser after closing an HTML pre segment.)