Two Techniques To Predict Urban Sprawl
Can we model urban sprawl with the same computational approaches used to model the evolutionary processes of biological organisms?
Cities are complex systems of systems, operated by countless processes on various levels and layers. On the physical level, the cities are nothing more than clusters of structures located very close to each other.
While the patterns of processes within individual cities may vary, there is one constant that is common for every city: the origin of the timeline. Be it London, Moscow, Beijing, New York, or Mexico City, specific locations, chosen by humans for settling and organizing their lives, sparked the onset of these processes for each city. Common considerations when choosing an origin location include access to natural resources, water, fertile lands, and natural defenses (mountain ridges, gorges, high-grounds).
Regardless of the reasoning behind the choice, the chosen origin location typically becomes a “power node,” attracting like-minded people with a common motivation to settle near and interact with each other. As civilization evolved over time, so did the processes of these interactions, reflected in the changes made to the areas surrounding the origin.
Why do cities sprawl?
When a city is founded, a power node forms. History may keep the node intact, and the resulting city will be classified as monocentric, or it may split the node, resulting in a polycentric city. In some cases, the node may be even dissolved, along the need of people to refer to the power node as powerful.
A node is important and powerful so long as people nurture it by organizing their lives and social interactions around it. The power node of New Amsterdam, established by Dutch, is still attractive and powerful, although people now refer to it as Wall Street. At some point during the 1860's, Central Park was constructed, leading to the accumulation of wealthy families around the area, introducing a second power node, now known as Midtown. Shortly after, New York City’s third power node was introduced with the construction of the Brooklyn Bridge, allowing people that claimed the new territories to interact with the main power node more efficiently. On a city scale, contemporary New York exists as a polycentric city with several large-scale power nodes and numerous smaller, satellite nodes.
The more important a node is, the more expensive (exponentially) it is to function close to it. The desirability of land close in proximity to these nodes results in more land being occupied and processed into urban areas. In other words, the nodes sprawl.
The processes of social interaction happening around a node, which “feed” the node and make it more important, are similar to those of fungi formation. When a fungus spore finds a perfect environment, it starts to consume the surrounding nutrients to sustain itself. At some point, it runs out of nutrients close by and has to grow and sprawl to reach the intact nutrients. Depending on the availability of nutrients, the fungi will either grow rapidly or its growth will be endangered by the shortage of supplies (think of urban markets and the similarity of the provision processes!).
Organisms evolve, and so do cities
Just as fungi need to grow to find fresh sources of nutrients to sustain themselves, healthy, growing cities with functioning power nodes sprawl to claim more resources. Of course, there are people behind the process of the urban sprawl, but once we imagine those people as providers of nutrients to the growing power nodes of the city, the two examples of sprawling systems (fungi and cities) start looking alike.
Biological organisms evolve from the simplest combinations of cells to vast complex systems of systems such as the human brain. Analogically, cities start from singular clustered structures and, in the event that the power node is effective, grow into networks of neighborhoods, boroughs and counties. The transportation network seeking the highest possible level of transportation efficiency evolves into network of roads, connected to avenues, connected to highways. Just like the vascular system of the human body, or the hyphal branches of fungi, it transfers the nutrients into and out of the city.
On genes and cells
Comparing urban sprawl with, for example, the hyphal growth of fungi, the question arises: is it possible to model the urban sprawl of a city by using the same computational approaches that are used to model the evolutionary processes of biological organisms? Of course, urban sprawl does not necessarily equate to the evolution of a city. Cities sprawl when the power nodes grow quickly, and the supply of housing close to the node is inaccessible to the majority of population. It is worth mentioning that cities do not only sprawl horizontally; their vertical growth can and should be considered a type of sprawl. While both Hong Kong and Mexico City have huge populations, due to the scarcity of available land, Hong Kong grows vertically, while Mexico grows horizontally.
Before speculating on the biological processes, let’s get ourselves familiar with two techniques of evolutionary computation:
- Genetic programming algorithms
- Cellular automata
Genetic algorithms are the way to computationally model the natural selection within a selected population. The population evolves when selected specimen produce a new generation via the genetic operators of elitism (the offspring carries the best genes of both the parents), crossover (the resulting genetic structure is the combination of swapped genes of parents), and mutation, which introduces a random gene in the structure. The mutation is usually kept at the significance level of 0.05% to ensure the diversity in the population, and that the function of fitness (the outcome of the genetic algorithm) won’t converge to a local optima, instead of converging to a global optima.
On the other hand, cellular automata (the singular is cellular automaton) represent the grid of cells, where each cell has a state. Out of numerous possibilities, when evolving, the cell decides which state to take based on a rule set. If we consider the binary states, when a state phenomena is either 0 (doesn’t exist) or 1 (exists), there are only 255 possible patterns of rule sets, also known as Wolfram rules. The evolutionary patterns of cells vary across the rule sets.
Evolution of urban areas
It is possible to model the sprawl of cities by analyzing the historical data of maps and giving states to every pixel. Thus, a pixel can have a state of a field, a road, a water surface, a building, a forest, etc. Based on the given rule set, the stateless cell will receive the state formed from the states of its neighbours. For example, if a cell is surrounded by cells that all have the state of a forest, there is a high probability, that the stateless cell will change its state into “forest”.
However, the problem (and the bias) with this approach is that the rule set is specified by the researcher, rather than emerging from a logical action-reaction mechanism of evolution. And that’s where genetic algorithms can help!
If the state of the cell (which can contain as many variables as possible) is its genetic structure, then that of the stateless cell can be specified via the genetic algorithm that will derive the fitness function converging to a global optima. That function itself is the rule set of cellular automata evolution!
Buildings as cells
Aforementioned techniques lead to speculating on a model that would allow us to predict the urban sprawl of a city with high accuracy. While we would certainly be interested in predicting the macro parameters of urban sprawl (such as the direction, intensity, and speed), the processes of urban sprawl happen on micro level as well. Just like the organism grows when its cells multiply, a city grows when new buildings are constructed. Factors such as the historical context of the development, geography, and policies (land use regulations, tax reforms, transportation changes) that shaped a certain growth pattern need to be considered as well.
What if the model considered buildings as cells that have genetic structures? Such a structure could consist of numerous variables, such as the average square foot price, different variables of the 311 data, variables representing energy efficiency of the building, etc. Then, it could be possible to form the genetic structure (the cell state) of the potential building that does not exist yet by using the states of its neighbors.
Next steps
While the theory is fascinating, it needs to be modeled and tested on practice. The steps following this article include the specifying of the datasets that can be included in the genetic structure of a building, modeling the cellular automata simulation of the urban growth, and testing the results on historical data of the development of the various urban areas.
