Fractal geometry (FG) is a branch of mathematics that instructively characterizes structural complexity. Branched structures are ubiquitous in both the physical and the biological realms. Fractility has therefore been termed nature's design. The fractal properties of the bronchial (airway) system, the pulmonary artery and the pulmonary vein of the human lung generates large respiratory surface area that is crammed in the lung. Also, it permits the inhaled air to intimately approximate the pulmonary capillary blood across a very thin blood–gas barrier through which gas exchange to occur by diffusion. Here, the bronchial (airway) and vascular systems were simultaneously cast with latex rubber. After corrosion, the bronchial and vascular system casts were physically separated and cleared to expose the branches. The morphogenetic (Weibel's) ordering method was used to categorize the branches on which the diameters and the lengths, as well as the angles of bifurcation, were measured. The fractal dimensions (D_F) were determined by plotting the total branch measurements against the mean branch diameters on double logarithmic coordinates (axes). The diameter-determined D_F values were 2.714 for the bronchial system, 2.882 for the pulmonary artery and 2.334 for the pulmonary vein while the respective values from lengths were 3.098, 3.916 and 4.041. The diameters yielded D_F values that were consistent with the properties of fractal structures (i.e. self-similarity and space-filling). The data obtained here compellingly suggest that the design of the bronchial system, the pulmonary artery and the pulmonary vein of the human lung functionally comply with the Hess–Murray law or ‘the principle of minimum work’.

分形几何（FG）是数学的一个分支，它具有启发性地描述了结构的复杂性。分支结构在物理和生物领域中普遍存在。因此，易碎性被称为自然的设计。人肺的支气管（气道）系统、肺动脉和肺静脉的分形特性产生了填充在肺部的大呼吸表面积。此外，它还允许吸入的空气穿过非常薄的血气屏障紧密地接近肺毛细血管血液，通过扩散发生气体交换。在这里，支气管（气道）和血管系统同时用乳胶橡胶铸造。腐蚀后，将支气管和血管系统铸件物理分离并清除以暴露分支。使用形态发生（韦贝尔）排序方法对测量直径和长度以及分叉角度的分支进行分类。通过在双对数坐标（轴）上绘制总分支测量值与平均分支直径的关系来确定分形维数（ D _F ）。支气管系统的直径确定的DF值为 2.714，肺动脉的 2.882，肺静脉的 2.334 _，而长度的相应值为 3.098、3.916 和 4.041。直径产生的D _F值与分形结构的特性（即自相似性和空间填充）一致。 这里获得的数据令人信服地表明，人肺的支气管系统、肺动脉和肺静脉的设计在功能上符合赫斯-默里定律或“最小功原则”。