SYSTEMIC RESILIENCE OF COMPLEX URBAN SYSTEMS ON TREES AND LEAVES

Two key paradigms emerge out of the variety of urban forms: certain cities resemble trees, others leaves. The structural difference between a tree and a leaf is huge: one is open, the other closed. Trees are entirely disconnected on a given scale: even if two twigs are spatially close, if they do not belong to the same branch, to go from one to the other implies moving down and then up all the hierarchy of branches. Leaves on the contrary are entirely connected on intermediary scales. The veins of a leaf are disconnected on the two larger scales but entirely connected on the two or three following intermediary scales before presenting tiny tree-like structures on the finest capillary scales. Urban system's structural resilience is highest when it is configured according to a scale free structure for its parts and for its connections. The spatial distribution and the intensity of connections in such a structure obeys a scale-free distribution. It states the frequency of an element's appearance and the span of a connection based on its hierarchic level: the smaller an element is, the more often it will be encountered in the system; the bigger an element is the rarer it will be. This fundamental law defines in itself the manner in which living organisms and things should be organized to optimize their access to energy, the use that they make of it, and their resilience. The history of urban planning has evolved from leaf-like to tree-like patterns, with a consequent loss of efficiency and resilience.