How nature takes shape: extensions of constructural theory to ducts, rivers, turbulence, cracks, dendritic crystals and spatial economics

The constructal theory of the origin of geometrical form in natural flow (open) systems began with the discovery that, contrary to the established view, the tree network can be deduced from a single principle: the geometric minimization of resistance in volume-to-point flow. This article reviews a series of developments that extend the constructal law over naturally shaped flow phenomena other than the tree. Examples include the proportionality between width and depth in rivers of all sizes, the nearly round cross-sections of all blood vessels and bronchial passages, the dendritic shape of the snowflake, the pattern formed by cracks in a solid that shrinks upon cooling or drying (e.g., mud cracks), the onset and multiplication of rolls in Be´nard convection, the transition (first eddy) and stepwise growth of all turbulent mixing regions, and the very existence of economics spatial structure (minimal cost routes between an area and one point).