Quasicrystalline Pattern Formation in Fluid Substrates and Phyllotaxis

Abstract

Phyllotactic patterns possess the quasicrystalline structure of the quasiperiodic Penrose tiling pattern. The author has shown that quasicrystalline structure of the quasiperiodic Penrose tiling pattern underlie iterative growth processes such as turbulent(small scale) fluctuations in fluid flows and round-off error growth in numerical integration schemes. Selfsimilarity in spatial structure extends down to the level of DNA molecules in plants . It is possible that plant growth processes may be coupled to the turbulent fluid environments of air and water respectively in the exterior and interior of the plant body down to sub-cellular levels resulting in the spontaneous generation of the quasicrystalline structure in plant growth pattern.