Fractal simulating a concentric city. Personal archives
Fractal analisis of Baila in Africa. Personal archives
This discipline is based on the chaos theory. We call chaos to everything that we are not capable of systematize.
In 1970, challenging the classic physics, some few scientists from United States and Europe began to look for an alternative route through the disorder: it was the beginning of the theory of the chaos. Mathematical, physical, physiologists, economists, chemical, biologists, tried to look for connections among different types of irregularities; they meditated that although there are phenomena that can be lineally described, -that is to say that the result of an action is proportional to its cause-, most of the phenomena in the nature is non-lineal, "uncontrollable", as the climate, the turbulences, earthquakes, the traffic in a great city, fluctuations in the bag, the physics of the human body, etc. The search for an explanation to all complex phenomena using mathematical models, originated the Chaos Theory.
The urban research was then related directly and formally with the natural world - the forms of the clouds, the arterial bifurcations, the lung texture, the groupings of stars, etc. All these shapes were described as opposite to the Euclidan ones, they were defined as folded, fractured. The word to define this conditions is “fractal” as opposed to “Euclidian”. Fractal is the geometry of nature; the geometric representation of the Chaos theory.
In 1970, challenging the classic physics, some few scientists from United States and Europe began to look for an alternative route through the disorder: it was the beginning of the theory of the chaos. Mathematical, physical, physiologists, economists, chemical, biologists, tried to look for connections among different types of irregularities; they meditated that although there are phenomena that can be lineally described, -that is to say that the result of an action is proportional to its cause-, most of the phenomena in the nature is non-lineal, "uncontrollable", as the climate, the turbulences, earthquakes, the traffic in a great city, fluctuations in the bag, the physics of the human body, etc. The search for an explanation to all complex phenomena using mathematical models, originated the Chaos Theory.
The urban research was then related directly and formally with the natural world - the forms of the clouds, the arterial bifurcations, the lung texture, the groupings of stars, etc. All these shapes were described as opposite to the Euclidan ones, they were defined as folded, fractured. The word to define this conditions is “fractal” as opposed to “Euclidian”. Fractal is the geometry of nature; the geometric representation of the Chaos theory.
A fractal has a very fine structure, it is detail in scales arbitrary small.
A fractal is too irregular to be described in the traditional Euclidian geometry.
A fractal has a certain kind of auto-similarity, approximate or stadistic.
The best example to illustrate a fractal, is a coliflower. It has a complex shape, and every small part is auto-similar to the whole.
For a city, we do not say the auto-similarity is perfect, we speak about tendencies to fractality.
The key of the understanding are the computarized images arisen from equations. The union between shapes and the world of numbers was an obvious rupture with the past.
The urban morphology is discontinuous, fractured and chaotic, with the same laws of organization of a biological organism. They seem to be examples of structures self-organized inside the chaos, as product of local actions (mutations) that imply some operation way until the process is stabilized.
The reasons above indicate that it would be insufficient to take an Euclidean geometric model to study the urban morphology. Instead of it, if we adopt a theoretical fractal structural model, we can study the morphogenesis of urban agglomerations and predict their possible future shapes in the aftermaths.
These autopoietic urban models can be verified with computer softwares of fractals generation and simulation of urban growth or dissapearance of urban tissue.
The creation of models is important in the understanding of the complex systems, since they can be built to test hypothesis or to create other new ones.
The models can be iconics, when they appear as what they represent (ex. an aerial picture that captures a scene) or, when the iconic models cannot be created, perhaps because the system that is represented doesn't have physical materiality, analogical models are appropriate. The models can also be a prediction tool. One of the validation methods, would be to enter initial data (input) in a model for which the final results are known and to compare them with the result (output) of the analogical pattern.
A fractal is too irregular to be described in the traditional Euclidian geometry.
A fractal has a certain kind of auto-similarity, approximate or stadistic.
The best example to illustrate a fractal, is a coliflower. It has a complex shape, and every small part is auto-similar to the whole.
For a city, we do not say the auto-similarity is perfect, we speak about tendencies to fractality.
The key of the understanding are the computarized images arisen from equations. The union between shapes and the world of numbers was an obvious rupture with the past.
The urban morphology is discontinuous, fractured and chaotic, with the same laws of organization of a biological organism. They seem to be examples of structures self-organized inside the chaos, as product of local actions (mutations) that imply some operation way until the process is stabilized.
The reasons above indicate that it would be insufficient to take an Euclidean geometric model to study the urban morphology. Instead of it, if we adopt a theoretical fractal structural model, we can study the morphogenesis of urban agglomerations and predict their possible future shapes in the aftermaths.
These autopoietic urban models can be verified with computer softwares of fractals generation and simulation of urban growth or dissapearance of urban tissue.
The creation of models is important in the understanding of the complex systems, since they can be built to test hypothesis or to create other new ones.
The models can be iconics, when they appear as what they represent (ex. an aerial picture that captures a scene) or, when the iconic models cannot be created, perhaps because the system that is represented doesn't have physical materiality, analogical models are appropriate. The models can also be a prediction tool. One of the validation methods, would be to enter initial data (input) in a model for which the final results are known and to compare them with the result (output) of the analogical pattern.
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