There seems to be some lack of clarity on how and where you can build improvements and resource nodes. So here's a guide, I guess, to how it all works.
Updated for 1.07
To do: Update to use the term resource horde since that's what Stardock uses
[ Definitions ]
Tile: One unit on the world map. If you have the grid turned on, those are 1 tile.
World Tile: Same as above.
Square: One buildable space unit. This is equal to 1/4th of a tile.
Space: Same as above.
City: What you build with pioneers. Anything within the city walls is considered a part of that city.
City Tile: A tile that is considered part of a city. A city tile is any tile with an improvement on it. Special case with resources (see below)
City Center: The initial tile that a city is founded upon. It will change appearance as the city increases influence and level.
Town Center: Same as above.
Enclosed: When something is surrounded by city walls and thus within the city limits. Improvements by default. Resources depend (see below)
Usable Space: A measurement of how much space a city has to build with. You can find this in the city detail screen. This is the same as Open Tiles and starts at 50.
Buildable Space: Same as above.
5-tile limit: The 5 square area away from a city that other cities or improvements can not be built within.
[ Building Limits ]
Every city has 50 squares of buildable space. This does not increase; you can always destroy buildings to free up space. Some buildings will take up 1 space while bigger buildings will take up 4.
Any part of your city counts as 'city' for purposes of movement. A unit can enter the city on any tile that is considered 'city' and leave on any tile adjacent to a 'city' tile. Thus if a unit enters a city that is 1x4 world tiles long from one end, they can leave on the other end at the cost of only 1 movement point.
Any part of your city counts as 'city' for purposes of defense and military engagements. Thus a unit trying to enter any part of the above 1x4 city would have to face the defenders with the city defense bonus.
Cities and improvements can not be founded or built within 5 tiles of another city tile. It is important to remember that this limit is based off city tiles not just the city center itself.
[ Improvements ]
Improvements can be built on any square bordering an existing city square. This can work on both diagonals and horizontal pieces. As with cities, they can not be built within 5 tiles of a different city square.
There are few restrictions to where you can build improvements. You can not build on non-walkable terrain (steep hills, mountains, and water). You can not build on beaches (other than the harbor improvement). You can also not build on forests. The latter are important; not all the tiles in the game are distinctly forest or beach; some of them may have only a few dead trees or such to indicate what they are. Thus it may see 'clear' but not actually be clear. You will need to use the terrain window (upper right) to check. You can build on swamps.
You can also build improvements outside your influence area as long as all other requirements are fulfilled. That is, if building it keeps you under 50 squares, and if it's far enough away from any other city's tiles, and it's next to another existing improvement, then you can build it even though it's outside the area of influence. If you do so, the tile with the improvement will produce its own influence for itself.
Improvements count as part of the city. As such, even if there is only one improvement on a tile, that tile counts as a city square for all intents and purposes.
2x2 buildings can straddle more than one world tile; they do not need to be contained into one world tile to be build. I've checked this on two tiles and need to check using 4.
[ Resources ]
Resource nodes are special and a result of a lot of confusion and ambiguity.
As long as a resource node is outside the city limits (it is not enclosed by the city walls), it is -not- considered a part of the city for any purpose. It only provides resources and can be attacked independently of the city. If there is an improvement within 1 square, a resource node will be enclosed. This makes the resource a part of the city for -all- purpose. It will count as city, allowing you to build improvements off it that do not connect to any other 'normal' improvement.
However, it will also count as a city square - thus allowing movement but also preventing building things within proximity. As of 1.07, resource hordes
Not Enclosed Resource: Provides resource, is not protected by city units, does not consume usable space, can not build improvements off, is not considered a city tile for purposes of the 5-tile limit.
Enclosed Resource: Provides resource, is protected by city units, consumes usable space, can have improvements built off it, is considered a city tile
Non-enclosed resources are built using their own independent building cue. Resources that would be considered enclosed are built using the city's queue.
What this all means is that resources can act in two different ways and change what they do depending on what you do. Most importantly for other cities, this means that a resource can change state from not-a-city to city. This in turn will change which tiles are considered within the 5 tile limit.
Resources -always- benefit from multipliers in the city it is linked to, enclosed or not.
[ Examples ]
( Example 1)
Say you have two cities (A and B ) with a resource (R) between them:
[A] [ ] [R] [ ] [ ] [ ] [ ] [B]
A and B can build improvements normally. They respect the 5 tile limit and they can build all around them. All seems well. A decides to build improvements towards the resource in order to enclose it. B also decides to build towards the resource for some reason.
[A] [X] [R] [ ] [ ] [ ] [X] [B]
The moment A finishes it's improvement, something -very- important happens. R is now considered part of A; it is now a city tile. This means that B is now -inside- the 5 tile limit by 1 tile. This prevents B from building more improvements on that side, regardless of space. If there is a forest or some such on the opposite side of B, then B will not be able to build in that direction either. This is because B is on the edge of the 5 tile limit but the tile past it is not.
( Example 2)
Here is another example (and probably more common). In this case, there are multiple resources near by and they are touching.
[A] [ ] [R] [R] [ ] [ ] [ ] [B]
[A] [X] [R] [R] [ ] [ ] [ ] [B]
A builds and encloses the nearest resource. Then, he builds the second resource; that encloses automatically since it is linked to the first resource which is linked to A.
Now, the both resources are considered part of A and a city tile. But, now, suddenly, look at the distance B is from A's city limits! B is not 1 but -2- squares within the 5 square limit. As a result, B can not build -any- more improvements since any improvement would be inside that limit. The only time B could do so is if B had build two improves in the other direction -before- A did. Note that resources that are not enclosed do not suffer from the 5-limit. So
[A] [ ] [R] [R] [ ] [ ] [ ] [B] [X] [ ] - B builds X and the player builds on both resources.
[A] [X] [R] [R] [ ] [ ] [ ] [B] [X] [ ] - A builds towards the first resource and connects them; again, both enclose since they touch.
In this case, B could then build improvements off the existing inprovements since that tile beyond them is outside the 5 tile limit.
( Example 3 )
Save you have a big city with 4 spaces left. You build a resource building that will cause it to be encircled. Since the resource is 'city', you will now have zero usable space left. If you have less than 4 spaces left, I don't know yet how the game will react but it may mean that clearing out a few buildings may not bring you over 0 again.
[ Special Note: Town Hall and Influence ]
The town hall and the empire equivalent increase influence, according to their description. What does that mean?
Influence is a hidden number that seems loosely based off prestige; that is, they seem to have close to the same growth rate. The amount of housing available determines how much influence a city can have. This in turn determines the size of the zone of control a city projects.
This radius is normally centered on your city center. Cities will produce a circle. Town halls act as a second city center, effectively projecting a second circle of equal size from their tile. Note that resources also must be within a certain distance of the city to be linked to it. This presumably affects that as well.
In effect, that level 1 city can grow it's zone of control without leveling up by using its improvements to span a greater width. The effect is also more noticeable in larger cities with sprawling layouts.
What these buildings allows a player to do is build cities further away from resources while still keeping those resources in range of the city. The question of whether you want to build in a cluster of resources or not depends on how big you want that city to grow, how much protection you want on those resources, and what not.
[ Special Note: Enclosed tile with no improvement on it ]
It is possible to create a city where a tile has no improvement on it but it is otherwise enclosed in the city walls. In this instance, the blank tile is not a city tile. A unit that walks into that tile will not enter the city. Therefore, in order for a tile to be considered a city tile, it must have an improvement on it. Resources, of course, only count as city tiles if they are enclosed.
Something to check out is enclosing a resource without actually touching it. My guess at this point is that it will not use up any city space and not be considered a city tile. However, with improvements all around it, it could effectively be defended for all intents and purposes as while no space around it holds an improvement, the world tiles around it would be considered part of the city.
I hope this helps clarify this.