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Is there a theory, model, technique that could help when placing cities on a map, instead of placing them randomly?

I have an estimate of the population for a given territory so I know more or less how many cities I'm supposed to have but I'm not sure how I should place them.

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    $\begingroup$ Not worthy of an answer - but I think terrain and setup (trade? farming? water/river? tactical? etc...) would mean more than an arbitrary standard distance. $\endgroup$ – Twelfth Nov 6 '14 at 20:13
  • $\begingroup$ A city is typically located at some waterway. So unless your mechanism makes sure this will be the case, it will not be very credible. Also, a junction of waterways is always a great bonus. $\endgroup$ – Burki Apr 15 '15 at 13:08
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Central Place Theory

As an Urban Planner, I could not help but put out there, the age-old Central Place Theory. It describes a hexagonal layout, and all other things are equal. It describes a generic urban settlement, that appears as a hexagonal assembly, and its relationships with other larger or smaller settlements.

It's generally well-accepted as a very high level conceptual diagram of trends in urbanism.

Other factors will include accessibility (your settlements should be on economically-accessible areas: trade routes or where there is economic opportunity) and it will do even better if there is an attractive climate - although that's not as strong a pull as the former.

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I'm basing this in part on my meh answer to another one of your questions. I think I can make this one better, though. By the way, I hope you didn't use my data for your estimates here; I seriously doubt it would produce accurate large-scale results.

Here are some places you could put cities:

  • Rivers: London, Paris, etc. Rivers mean transportation; transportation means trade; trade means a strong economy. Rivers also mean source of fresh water, as well as fish. Although I think we'd all get sick of flounder after a few days.
  • Ports: Boston, New York, Rome (indirectly), Hong Kong, etc. Ports mean long-distance trade, and long-distance travel. Until your species can travel via the air, water is going to be important (this hearkens back to my section on rivers). Jason Patterson also raised an excellent point: Settlements will spring up wherever roads meet water. This can include points by a river where two sides are the closest, or the narrowest part of a lake.
  • Mountain Passes: Strange but possibly true. Let's say you have a city at point $A$ (done in LaTeX for dramatic effect) and a city at point $B$. Point $C$ is in the middle of a mountain pass, right in between the two. I can assure you that people from both cities will want to build a settlement there to control travel and trade between the two. Think a land-based version of the Bosphorus and the Dardanelles.
  • Lakes: Back to the water. You've got water, you've got fresh food, you've got some land - who could ask for anything more? (Corny, I know.)
  • Wherever there are roads: You aren't going to have a city where there aren't any roads. Try spots that are in places where roads meet open fields or flat ground. These junctions may also provide arable land.
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  • $\begingroup$ In particular with regard to rivers and roads, the places where these meet are likely to have settlements. The confluence of two rivers is a good place for trade. The location of a bridge, ferry, or ford is a site where people are almost certain to live. Villages grow into cities over time. $\endgroup$ – Jason Patterson Nov 7 '14 at 20:16
  • $\begingroup$ @JasonPatterson Excellent point. $\endgroup$ – HDE 226868 Nov 7 '14 at 20:19
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Unless you are working with a planned nation, i.e. leaders started it from scratch kind of like a planned city, distance is not particularly relevant when assigning locations.

I think it important to define a city...which may seem ludicrous but stick with me.

  • City: A collection of people and structures with socials services, and defenses in a contained, contiguous geographic area.

Why bother defining it? Well if you look at some situations, for example Minneapolis/St Paul, its pretty easy, with the exception of politics to call that one city and for the sake of map building you can consider it one city, even if you later break it apart for political or localized geographic reasons.

So, moving on to your question.

Is there a theory, model, technique that could help when placing cities on a map, instead of placing them randomly?

Not that I am aware of, but luckily we don't need one.

  • Start with a map. If you have your map you can get a solid idea of where cities should be placed. This map needs to be fairly detailed, you need to know the terrain, the major bodies of water, the local climate...is it arid, or temperate, how much rainfall etc etc etc.

  • The first cities: Once you have your map find good geographic locations for settlements, as HDE mentions water is huge. The first (and oldest) settlements you place are simply going to be locations that have all humans need to settle and grow a town.

  • Non agrarian cites: These will develop along trade routes, or at strategic points. (cross roads, passes, river crossings, holy sites) This question may help you as well: How can I ensure my cities don't all look the same?

  • Keep resources in mind. As mentioned in step 1, you have to know your map. Your question is right in assuming that you can only have population centers so close together. This is why. Only so many people can live so close together...though perhaps the population of two nearby large cities are overwhelming local resources...which leads to conflict, which leads to a good story setting...

You are better off applying logic here rather than a mathematical formula. Just try to consider how things developed. First you had mainly nomadic peoples, hunters and gatherers. They wandered and perhaps picked and ate corn, maybe eventually they noticed it grew in the same place every year. You start a settlement where food and water are plentiful and shelter is available. Rather than being nomads you now have a small village and hunters that range out from the center. Agriculture develops. This happens all over the area with splinter or other totally isolated groups. Eventually as things grow people interact and trade. Common paths develop. Pull the thread. Its a fun trip.

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I couldn't find a reference online, but I vaguely remember that they did a study and if you take a fairly featureless landscape and assume most travel is done by foot, then settlements tend to be about 6 miles apart.

Terrain will affect this, mountains, and hills, valleys, rivers and lakes etc. Roads connecting them will follow the easiest routes.

Better transport, roads, rivers etc. will increase the interconnectedness of communities and trade will follow the easiest paths, or connect the most desirable commodities to their markets.

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  • $\begingroup$ are you talking about the central place theory? If you could develop it, it would be a very good answer! $\endgroup$ – Vincent Nov 10 '14 at 4:56
  • $\begingroup$ @Vincent that looks about right. I'll try to expand this later to incorporate it. $\endgroup$ – bowlturner Nov 10 '14 at 13:41
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The settlements would be focused around resources or crossroads for the most part.

Start with the landscape, and built up. Think about the resources required, easy access to wood, farming, water, etc.

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