In the 20th century, the modern movement in architecture drew up grand plans to remake cities for the machine age. Le Corbusier, the leader of the movement, conceived his Radiant City plan. He designed every part of it himself so that it would work as he had willed it to. His machine provided the solution to four problems: inhabitation, work, recreation, circulation. Everything else was removed.
The idea of a machine city expressed three assumptions that led to the catastrophic results of modernism.
The first assumption is that the city is a machine that solves a problem. It can then be designed as a tool would be.
The second assumption is that the will of a designer can be imposed at the scale of a city.
The third assumption is that the form of a city, its morphology, can be conceived in advance of its development ("planned").
After a titanic fight over the future of New York City, Jane Jacobs explained this error in the final chapter of Death and Life of Great American Cities. The "kind of problem a city is" shares nothing with the physical and engineering sciences. It is like the biological sciences, a problem of organized complexity.
The city does not solve a problem or some problems, it provides the environment to solve the infinite diversity of little problems that human beings have.
It is so complex that no single human can ever hope to understand it entirely.
Its morphology must be defined by its growth process as it adapts to changes in human needs and desires.
The city cannot have a designer. It cannot be built according to a description fine-tuned to perfection. This has become obvious to practically everyone, although urbanism in the english-speaking world is still tied down by the title "urban planner" in the face of all the evidence that planning makes no difference whatsoever. Still the practice of large scale zoning and site planning continues.
The problem was the absence of an alternative theory.
Today this theory exists. Research into DNA and cellular automata has shown how systems of transformations, as opposed to descriptions, create complexity in nature through emergence. Cells which multiply themselves and interact following simple sets of transformation rules produce forms of astonishing complexity.
A system of transformations is similar to a recipe. It is a list of actions that you must take, as compared to a descriptive system which gives you a picture of a finished object. Imagine trying to bake a chocolate cake with nothing but a picture. Now try again with no picture but a full recipe. By following the recipe, you will get a tasty cake no matter what mold or size of cake you made. If you make a mistake in the recipe, your cake will not succeed.
The definition of emergence is thus: it is a form obtained as a result of following certain processes. The opposite of emergence is design: it is a form conceived by a designer which will be used as a blueprint for its realization.
In emergence, form is the result. In design, form is the starting point.
The 21st century paradigm of urbanism is discovering and applying the right recipe, DNA, transformation set, to build a city, at any size, shape, or starting point, so that it will always work, always be adapted, and always be full of life.