STREETS TREE NETWORKS AND URBAN-GROWTH - OPTIMAL GEOMETRY FOR QUICKEST ACCESS BETWEEN A FINITE-SIZE VOLUME AND ONE-POINT

The geometric form of the tree network is deduced from a single mechan ism. The discovery that the shape of a heat-generating volume can be o ptimized to minimize the thermal resistance between the volume and a p oint heat sink, is used to solve the kinematics problem of minimizing the time of travel between a volume (or area) and one point. The optim al path is constructed by covering the volume with a sequence of volum e sizes (building blocks), which starts with the smallest size and con tinues with stepwise larger sizes (assemblies). Optimized in each buil ding block is the overall shape and the angle between constituents. Th e speed of travel may vary from one assembly size to the next, however , the lowest speed is used to reach the infinity of points located in the smallest volume elements. The volume-to-point path that results is a tree network. A single design principle - the geometric optimizatio n of volume-to-point access - determines all the features of the tree network. (C) 1998 Elsevier Science B.V. All rights reserved.