Spontaneous Emergence of Long-Range Shape Symmetry

Self-organization of matter is essential for natural pattern formation, chemical synthesis, as well as modern material science. Here we show that isovolumetric reactions of a single organometallic precursor allow symmetry breaking events from iron nuclei to the creation of different symmetric carbon structures: microspheres, nanotubes, and mirrored spiraling microcones. A mathematical model, based on mass conservation and chemical composition, quantitatively explains the shape growth. The genesis of such could have significant implications for material design.