The new study explains mathematically the scaling laws of cities.
An example of the law of scaling cities is the number of gas stations: if the population doubles in a city with 20 gas stations, then the number of gas stations increases not to 40, but only to 36.
This growth rate is approximately 0.80 and applies to most of the city’s infrastructure. For example, energy consumption per person or area of a city only increases by 80% for every doubling of the population. Since this growth is slower than doubling, it is called sublinear growth.
On the other hand, cities are showing more than double growth in other directions: the amount of money in the same job, the number of phone calls, and even the pace of walking are increasing. This super-linear growth rate is around 120%.
In order to understand where these 0.8 and 1.2 come from, the researchers first mapped the place where people lived on a three-dimensional map. Then they used open data on the height of buildings in more than 4,700 cities in Europe and assigned a place of residence for each person and called such associations human clouds.
Zooming in to human clouds looks like a coherent whole. Based on these human associations, the researchers were able to determine the fractal dimension of a city’s population, or the ratio of change in detail to change in scale. As a result, they obtained an average value that describes the human cloud in each city. In the same way, they calculated the fractal dimension of the urban road network.
The authors found that these data are very different, but their ratio is always approximately the same. The authors believe that their discovery will help to build cities correctly and design technological spaces without harming the comfort of the population.