This geometric principle is applied in many man-made and natural systems. Ultimately, an optimal rectangular shape can be found to minimize the thermal resistance between the element and the exit end of its high-conductivity fiber. The same geometric-optimization principle applies at larger scales. The next volume is an assembly of optimized volume elements of the smallest size. The process of construction and shape optimization continues toward stepwise larger scales until the given volume is covered.
Tree networks abound in nature, in both animate and inanimate flow systems.
Every detail of every natural tree, for example, can be anticipated through the construction and optimization shown for the heat tree already discussed. The high-conductivity channels form a tree. More important, each feature of the tree is deterministic, the result of a single principle of optimization. This conclusion runs counter to currently accepted doctrine that natural structures are nondeterministic, the result of chance and necessity. But fractal geometry is descriptive, not predictive.