Skip to 0 minutes and 10 secondsAre we willing to consider the urban to be non-linear as well, the urban behaving as a complex, adaptive system? Two names are, in this respect, important-- Walter Christaller and his static proposal of a multi-layered urban world, and Benoit Mandelbrot showing us how a dynamic fractal-like reality could look like. Let's first look at Walter Christaller. In 1933, a long time ago, he came up with a quite interesting theory. We call it a central place theory. It shows a rhythm between cities, towns, and villages, a hierarchy of human settlements. It's a slightly aesthetic model. But it is a fascinating model too because it relates very much to non-linearity and to multi-level patterns, patterns of emergence which result in various kinds of specialization.

Skip to 1 minute and 11 secondsI'll give you two examples. One is a supermarket. You'll find it in every village, town, and city. A supermarket is a generic function. However, you won't see everywhere what is luxurious, specific, and expensive, for example, the piano shop. For this kind of products, you do not go to just every coincidental village. Pianos are most likely found in the center of the main city. It makes perfect sense. But you have to be aware of this rhythm. A city is an interesting phenomenon. A city is far from stable, with one city not being the same as the other. Christaller showed us there are patterns of cities being connected, nonlinear patterns which differentiate cities from towns and villages.

Skip to 2 minutes and 3 secondsThese patterns are not fixed or frozen. Through time, we can see patterns of cities evolving. A long time ago, cities were just nodes on crossings. It is where you can cross a river easily or where two roads meet. There, you will find a beginning of a city. Later, cities became marketplaces, being a new entity with new functions and structures. Consequently, cities became safe havens with walls around it for protection. Since the Industrial Revolution, we consider cities as places of production and consumption, a source for labor, and a mechanism to generate capital. Nowadays, we see this entirely different again. And places and spaces are now there for communication, interaction, and creativity, centers of democracy even.

Skip to 2 minutes and 58 secondsAnd we appreciate these spaces is being leisurous, pleasant places to be, and quite often, surprising places as well.

Skip to 3 minutes and 7 secondsWith possibilities to discover with flows, dynamics, et cetera, these places are there where the local and global meet. And what is really fascinating of all these examples of evolutionary patterns of cities is that cities hardly disappear. London has burned down three times, but this is still there. Cities do not evaporate. They are robust, while at the same time, they are very flexible. If we look at these changing patterns more in depth, we see jumps we could call transitions. With these jumps, the structure and function of the city change altogether. They co-evolve, which gives the city an entirely different meaning through time. And that is fascinating. Mandelbrot proposed a dynamic sequence which is non-linear. His sequence is called a fractal.

Skip to 4 minutes and 8 secondsEach step in his sequence is a repetition of an earlier step, resulting in disproportional, non-linear development. It's also a process of self similarity, which we see as well within cities. And this self similarity is also the key to Mandelbrot's fractals. At whatever scale the fractal is being looked at, it reproduces the same structure. And that is fascinating. Mandelbrot's fractal is both dynamic and multi-level as a city is.

Skip to 4 minutes and 44 secondsCould Mandelbrot's idea of non-linearity become an interesting way of looking at a city's development in the future? Will non-linearity help us to understand the city better than we did before? And can these mathematical structures help us in understanding non-linearity?

Skip to 5 minutes and 9 secondsThe city of past is no longer the city that is today. And the city today will not be the same as the city of tomorrow. And what the city of tomorrow will be is almost impossible to predict because structure and function will co-evolve together. That's the excitement of the city evolving in a non-linear way.

Urban non-linearity

This video describes how we can find non-linearity in the urban.

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Decision Making in a Complex and Uncertain World

University of Groningen

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