Complexity Theories of Cities (CTC)

  • Juval PortugaliEmail author
Part of the Understanding Complex Systems book series (UCS)


Henri Bénard, a French physicist working at the beginning of the 20th century, found the following about a liquid in a round vessel heated from below: At the beginning of the process, when the temperature difference between the heated bottom and the cool top is low, the heat is being transferred by conduction and no macro-motion can be observed in the liquid. However, as the temperature difference increases and a certain threshold is reached, the movement in the liquid becomes instable, chaotic and then a strikingly ordered pattern appears: The molecules of the liquid which at the beginning were moving in random, suddenly exhibit a coherent macro-movement in roles which are millions of times larger than the molecules. As can be seen in Fig. 4.1, the motion of the roles forms a hexagonal pattern on the surface of the liquid. This pattern is in fact an outcome of the movement of the hot liquid, which rises through the center of the honeycomb cells, and of the cooler liquid, which falls along their walls. All this happens as if by an external force. Yet no such force exists – the spatial order appears spontaneously, by means of self-organization.


Fractal Dimension Cellular Automaton Cellular Automaton Complexity Theory Dissipative Structure 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  1. 1.Dept. of Geography and the Human EnvironmentTel Aviv UniversityTel AvivIsrael

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