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I prefer the so-called 3x3 grid; and I notice that the center square often does not build. I have added to several towns an extra road piece (one of the side squares) to give road access to that center square; yet it still does not build, even after all other squares in the same block have built and blocks more distant from town center are well built, too.

Meanwhile, a town constantly adding population will, on occasion, build on a square that has not got road access; the new building may be a square away. This can happen if towns are not allowed to build their own roads and player doesn't build them, either.

So road access, while it seems to contribute, is neither necessary nor sufficient for a new building.

It's certainly clear that a well-serviced town grows quickly while an unserviced town hardly grows at all. So station service to the town is vital. But should a square fall within some serviced station's catchment area to build? Again, I've seen growth outside of any catchment area so this is not necessary; but perhaps it's a particular incentive.

Does terrain affect building? That is, is building on a square encouraged or discouraged by rough terrain, trees, slopes (building on slopes enabled), rocks, or freshly cleared bare land?

What other factors affect the likelihood that a given square will build?

Game mechanics is silent on this topic. Browsing forums turns up a scattering of information, much conflicting and some almost certainly wrong. What's the truth?

2012-02-12: Experiment suggests a square may be more likely to build if two or more road tiles are adjacent -- meaning any of the surrounding 8 squares. A single adjacent road tile provides little or no incentive; two may be barely sufficient; three or more encourages. So corners of a block, which are adjacent to 5 road tiles, often build first. Note that a single straight road provides 3 adjacent road tiles. So I've been running an extra road in newly developed town (I never allow town to build roads), cutting the block down to a 2x3. When the center square builds, I remove the extra road. This works... sometimes.

2012-02-14: Some forum posts suggest that towns want to build "evenly"; that is, they will avoid building on squares more distant from town center until squares are build nearer. This is a stronger statement than merely to say it's more likely that a near square will build than a far square: near construction gates far construction.

Example: I'm now seeing two towns, roughly alike, both bounded by water, each composed of 4 blocks. In one, town center is equidistant from the sea on all sides; in the other, town center is a corner almost sticking out over the water. The former grew, the latter does not, despite all encouragement for 30 years. There is one big buildings in that one off-center-center corner; all the rest is small houses and vacant land.

I'd like to see this confirmed in source. Towns will build far before near is absolutely solidly built; what's the function?

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this question may provide some info as well –  z - Feb 8 '12 at 13:27
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Update: After examining in detail a function on line 2166 of town_cmd.cpp, it is my opinion that the town chooses the building completely randomly based on two factors: the tile's "status" (which just controls whether a tile is 'available' for building on) and the town's "radius group". This is also corroborated by my experience in-game, which is that towns will build different types of houses based on how big the town is and which 'ring' the tile is in. Hopefully this is what you wanted, but I'll preserve the rest of my answer in case anybody else finds it useful.

Update 2: After reading your comment, I feel compelled to point out that the below paragraph should answer that question (on road access). Having said that, I'm a bit confused since I've never experienced the problem you're referring to - admittedly I greatly prefer "original" layout over 3x3 grid; perhaps it's simply my lack of experience in 3x3 grids that has caused the greatest amount of confusion in regards to this answer - for that, and the lack of organisation/coordination in later editions of the answer, I apologise.

It is my belief that for a square to build it must have road-access (otherwise the town will build a road for it), 'road-access' is defined by a road within 2 squares (ie an adjacent square must be a road). There is no particular way to build roads that will encourage or discourage building on a particular square - the town requires it, but will build the roads itself if necessary. There's no way to "force" a town to build in a particular square.

If you disallow town road-building, you will need to fill in road access according to the above rules in order for a square to build (road within 2 squares).

The old (fairly off-topic) answer:

I've played the game for a number of years now, and probably can't offer anything more definitive than said sources but I'll give it my best shot anyway.

The bit in bold is there because it is the factor that keeps cropping up in code, and I think is the most important factor in growth. If the town has not reached its goal, it will not grow (unless you are funding its growth).

Also worthy of note: funding a town twice in a row doesn't appear to be economically-sensible. It seems the town will be funded for growth for the next 3 months at the point you fund it - funding it again will not increase this to 6 months, it stays fixed at 3 months. The second funding is, therefore, wasted. (this is according to my interpretation of the source code)

The following factors affect whether a square will be built on [source confirmed]:

  • Terrain: square must be flat (unless an option for building on slopes is enabled)
  • Bridge: square must not have a bridge on it.
  • Road: square must be within 2 squares of a road
  • Building: square must not already have a building on it

According to the code as I've read it, these are the only factors affecting whether a specific square will be built on or not. As for when a square will be built on, see the rest of my answer about town growth rate (a much more complicated topic).

The following factors affect how quickly a town grows:

  • [source confirmed] The Local Authority option "fund new buildings" will cause the town to grow on the next tick and every tick for the next 3 months.
  • Terrain: flat terrain at the same level as the rest of the town is favoured over any other type, and squares are then chosen, it seems, by how close in level the terrain is.
  • [source confirmed] Town size: larger towns grow more quickly
  • Resources: passengers are one thing, but towns also grow faster if you ship goods, valuables and mail to them - in some terrains other things such as water will affect town growth
  • Road grid type: towns with 'original' layouts grow faster because they are less restricted in where they place their roads - note that towns will avoid building roads on sloping terrain more than they will avoid building anything else there (meaning you want to let them build roads however they want)
  • [source confirmed] Towns have a 'goal' of how much cargo needs to be delivered, when this goal is reached, the town will grow by a set amount.
  • [source confirmed] Time: towns will wait a set amount of time in between placing houses, when the time is up, it appears the town makes a decision based on other factors whether to (and where to) place a house.
  • [speculation based on source code] Nearby towns: it's possible that nearby towns hinder growth (yet to confirm, will need to read more)

The following things appear (to me) to be a placebo affect at best:

  • [source confirmed] "Helping" with road construction: the town, during its 'growth cycle', will automatically build any necessary roads - if there are already roads, the town will grow as if it built the roads itself. It may save you one or two ticks for a road to become fully built, but the time it takes for you to build the road isn't really worth it.
  • Shipping cargo away from the town: doesn't appear to have any affect on town growth speed, except that if you're shipping away then you're usually also shipping to. Experiments prove inconclusive.
  • Shipping cargo to local industry: inconclusive, this may or may not aid town growth - experiments have yielded differing results (perhaps some industries are better than others, many more experiments would be necessary to determine this and/or examination of the code).

The following factors definitely have nothing to do with town growth (but are worthy of note since many people think they may help/hinder):

  • Nearby railways, highways, etc.: towns don't much care about vehicles going near to them - just stations. From what I've seen, as long as the track/road/whatever isn't close enough that it directly impedes growth, it's fine. In fact, many times I've seen towns "gobble up" nearby railways by building across them. [source note] bridges and tunnels do affect whether or not a town will build on a particular square, and can be used to "pen in" towns, but will not affect the town's overall growth speed (and towns may 'escape' these pens, I've yet to experiment with that).
  • Using different classes of vehicle: surprisingly, some people think using more expensive vehicles has an affect on town growth. I've never seen any evidence whatsoever to support this.
  • Taking resources away from local industry: taking wood from a local forest, for example, may aid slightly in growth but I've not seen any significant impact. It certainly doesn't, as some people believe, hinder growth.
  • [source confirmed] Local Authority rating has nothing whatsoever to do with town growth. When the LA rating is modified in town.cpp, the code does not do anything to the town's growth rate. People may have this misconception due to the fact that towns that the player's company has high LA rating with grow faster because they're serviced better by the player's company. Same is true of non-player companies.

This answer is meant to be comprehensive but may not be exhaustive. I will come back and improve on it later on, when my girlfriend lets me play again (something about "becoming obsessive"... I dunno what she means, I mean 10 hours a day is healthy... isn't it?)

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Stopping for today, I will add a note here that the function I'm currently looking at can be found on line 1115 of the file 'src/town_cmd.cpp' and is called GrowTownInTile(). I'll return to that later, I think! Hope this helps, anyway, and like I say I will continue to improve on it! –  Chris Browne Feb 11 '12 at 10:28
    
I'm awarding you the bounty but not Best Answer... yet. Keep working on it. –  Xiong Feb 12 '12 at 9:33
    
thanks :) I will. –  Chris Browne Feb 12 '12 at 10:13
    
gonna take a break again, I've done another 30 minutes or so of work - it is a sunday though! I'll come back to it tomorrow. Hope it's progressing towards what you were expecting/wanting :) –  Chris Browne Feb 12 '12 at 10:52
    
Please remember the question is about town buildings: whether town will erect a house, shop, office on a given square. I never allow town to build roads; a big part of this question concerns how I should build roads to incite town to build near them. –  Xiong Feb 13 '12 at 9:06
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