Ever since I was young, I've been playing SimCity. I first started playing the original version in the early Nineties, and then graduated to SimCity 2000. I then jumped ahead much later to SimCity 4, but found it too complex for my tastes, though it did seem very pretty. So I gave it up.

With the recent news that the SimCity franchise has not been left for dead, my nostalgia for these games has been rekindled. I can remember poring over the information and references about urban planning and the nature of cities included in the original SimCity manual. I recall waiting for hours while playing in order to have enough money to construct an airport, or seeing what the smallest sustainable city with a positive cash-flow it was possible to create.

Since my days playing SimCity, I've become involved in scientifically understanding cities, which is a rapidly growing field. I've looked at how individual interactions affect the productivity and innovation of cities, and how different types of prosocial behavior scales with the size of urban populations.

Well, I've finally been able to combine these two loves of mathematics and SimCity. As discussed in an article over at The Atlantic Cities, I explored how to calculate the complexity of a city, specifically its Kolmogorov complexity, using SimCity:

...we can easily use SimCity to measure a city’s Kolmogorov complexity, because we have files for each simulated city in SimCity. And each file is a city’s complete description, so its file size is, in a rough sense, a measure of its complexity. Using a small dataset of population sizes and file sizes of some cities constructed in SimCity 3000, I checked to see how complexity scales with population size. It turns out that urban complexity scales linearly with population:

What this means is that for each additional simulated individual in a city, the algorithmic complexity increases by a constant amount.

You can read the rest of my exploration of the complexity of cities via SimCity here.

And as a bonus: another example of using science and mathematics to delve into SimCity is the theory that underlies the creation of the city Magnasanti. The brainchild of Vincent Ocasla, Magnasanti is the scary outcome of what happens when you try to "beat" SimCity 3000 through years of equations and graph paper drawings: six million residents, no water pollution, no traffic congestion, no crime, all in the package of an unbelievably dense hellscape. It is the largest population sustainable:

Clearly we need more mathematical analyses of SimCity.

Top Image: Sancho McCann/Flickr/CC