Mimicry in plants and animals. The discourse's central chapter features examples and observations of the quincunx in botany. Rand Worldwide you can read the original papers that demonstrate convergence. 84 The fissured pattern that develops on vertebrate brains are caused by a physical process of constrained expansion dependent on two geometric parameters: relative tangential cortical expansion and relative thickness of the cortex. "Gyrification from constrained cortical expansion". Koshy uses (page 78) phi.6180339. For example, when leaves alternate up a stem, one rotation of the spiral touches two leaves, so the pattern or ratio is 1/2. "Growth in Plants: A Study in Number" (PDF). General books edit Adam, John. Fibonacci Web site (ott/Fibonacci/ml) where there are many more details and explanations with applications, puzzles and investigations aimed at secondary school students and teachers as well as interested mathematical enthusiasts. 79 :6 More elaborate models simulate complex feather patterns in the guineafowl Numida meleagris in which the individual feathers feature transitions from bars at the base to an array of dots at the far (distal) end.