Adrian Bejan | Forest and Natural Hierarchy, from Design in Nature
The video describes how a piece of ground with the freedom to change arranges trees so that water flows from the ground into the air more effectively, and how this tendency creates a natural hierarchy in the forest, with few large canopies and many small ones. It imagines the forest as a patchwork of elements, first shaped as equilateral triangles and then as squares, each element containing trees of various sizes, labeled D0, D1, D2, D3, and so on. On each fixed area, the sizes of the canopies become smaller while their numbers become larger, as new armpits appear between existing canopies and invite smaller vegetation to grow. The same idea is then expressed in a log-log plot of canopy size versus rank, which shows populations grouped into bands, indicating that smaller individuals are more numerous. The video connects this prediction to maps of cities over Europe and to real fields and orchards where shrubs and weeds appear in neglected spaces. In this way, it is concluded that hierarchy is a natural phenomenon that follows from the ground's freedom to change its configuration and move water upward.
The video begins with a law stating that the water flow rate per unit area in a larger region depends on the size and number of tree canopies present, and benefits most from large trees. It represents one forest element as an equilateral triangle of length scale X and places one large D0 canopy in it, leaving armpits where smaller D1 and D2 canopies can grow and become more numerous.
It then repeats the construction with a square area element of side X, placing a large D0 canopy in the middle and showing how the armpits around it are filled with smaller D1, D2, and D3 canopies. As the sizes decrease, similar contributors become more numerous, and armpits proliferate rapidly.
Next, the video shows that even if the first canopies in the square are not the biggest possible, one can start with several big D0 trees at the corners. This arrangement places another large tree, D1, in the middle, then larger armpits for D2, and finally a large population of small D3 trees.
All these imagined populations are then plotted on a log-log scale, with the ordinate showing the length scale of the projected canopy and the abscissa showing the rank of each size. The horizontal bars formed by these points show that each population has few large and many small members and that hierarchy emerges naturally from the construction.
The video notes that the same drawing appears in the distribution of city sizes and ranks across Europe, which also sends water and other materials back into the wind. It then turns to agriculture and orchards, where young shrubs and weeds always appear in the spaces between planted canopies, because neglected ground tends to reconfigure itself to direct water upward more effectively.
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