The consequences of contact pressure in phyllotaxis

摘要: Abstract To determine the consequences of contact pressure in phyllotaxis, a mathematical model is constructed which leaf distribution represented by point lattice n + 1 points at equal intervals on helix wound around cylinder. The normalized taking girth cylinder as and measuring time T plastochrones, so that = [T]. r stands for internode distance (component between two consecutive parallel to axis cylinder). d divergence (fraction turn points). It assumed monotonic decreasing function such r(T) → 0 ∞. Contact assumption minimum geodesic maximized. shown if (p, q), with p t 2 … (a x) determined q converges an ideal angle τ , where golden section. A necessary sufficient condition be −2 initial phyllotaxis Fibonacci numbers sequence 1, 2, 3, 5, 8, …. proved convergence τ−2 normal begin before 5 or 3 38 initially .