![]() In this example, the scientists heated a mixture of SiO and Ag 2O to prepare the silver-cored, silicon-dioxide-shelled microstructures onto substrates at 1270 K, a temperature above the melting point of silver but below that of silicon dioxide, in order to achieve the proper elasticity difference in the subsequent cooling process. On an elastically mismatched structure, which consists of a stiff layer on a compliant surface, a variety of buckling occurs. In their experiment, the scientists used a technique from stress engineering, which is often used for the mass fabrication of micro- and nanostructures. Because their microstructures were very small, the next series (21x34) would have required more than 700 “spherules,” creating so much stress that the structure would break. For example, Li, Ji, and Cao produced a series of spirals of 3x5, 5x8, 8x13, and 13x21. The numbers of spirals on a surface are two consecutive numbers in the Fibonacci sequence (1, 1, 2, 3, 5, 8, 13, etc.). The patterns consist of spirals that curve around a surface in both the “sinister” form (clockwise) and the “dexter” form (counterclockwise). This is the best support for this energy principle of phyllotaxis (or “leaf arrangement,” often credited to D'Arcy Thompson) before a rigorous mathematical proof is available.”įibonacci spiral patterns appear in many plants, such as pinecones, pineapples, and sunflowers. Our experimental results provide a vivid demonstration of this energy principle. “We conjecture that the Fibonacci spirals are the configuration of least elastic energy. “Patterns that evolve naturally are generally an optimized configuration for an assembly of elements under an interaction,” Cao explained to. ![]() Scientists conjecture that Fibonacci spirals are the least energy configuration on conical shapes. ![]() Fibonacci spiral patterns grow on conical-shaped microstructures, shown above in the sinister form. ![]()
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