way #1: people naturally settle in places with useful natural features, and a village -> town -> city develops over time organically, just people building new buildings as they individually need them.
way #2: the state uses public funds to plan and build a whole city from the ground up. Individual buildings or the rights to build on plots are sold to landowners or developers, within the plan laid out.
Most of the time there’s a little of both. All states regulate construction at least a little, and sometimes massive changes are made to a city for the public good.
This is a ton of ways to approach this question, so I’ll take the centuries portion.
Look at Las Vegas. It was a bare spot of desert where some rail lines met. There was water, so the opportunity for commerce and survival meet.
Incorporated in 1911, it blew up population-wise in the 1930’s with its proximity to the Hoover dam and jobs. Then in the 1980s the population just about doubled, from 180k in 85 to 360k by 95. And then it’s doubled again since to close to 700k residents.
It was less about the state and more about opportunity for private industry. There was money to be made so people moved there, corporations built up the area, the population grew as did the tax base which supports the public works.
TLDR; if there is money to be made, people will move there and build things. Cities are less planned and more form to fill an economic need.
Generally a state or country doesn’t develop a city. Typically people choose to start living in a location together due to a combination of water, timber, fertile soil, location, transportation, food sources, climate, beauty, etc.
Over time this settlement attracts other settlers due to network effects of the what the improvements the earlier settlers make.
If you look at a map, and follow a river or railroad, you’ll notice towns and cities spaced around one days travel on foot or by wagon, or at a relatively safe stopping point after a natural barrier like a mountain pass or edge of a desert.
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