The principle represents the physics behind fractals, the reason why natural tree networks happen to look like the truncated fractal images postulated by mathematicians. In the past, the minimization of travel time has been invoked to account for the shape of light rays. Research as far back as Heron of Alexandria has shown that when the ray strikes a mirror, the optimal angle of incidence equals the angle of reflection. We were also taught that the ray is bent to an optimal angle as it passes from one medium into another. It bridges the gaps not only between physics, biology, economics, and many related fields but also between physics and engineering.
Nature is the supreme form of engineering design and organization.
N.C. This research was supported by the National Science Foundation.