Phyllotaxis and patterns on plants

Amplitude Equations 1. Representationw(r, α, t) = ∑ A s m(r, t)e is ∫ l mdr−imα + (∗)where A m (r, t)e i ∫ l mdr is WKB approximation for Hankel functionsH s m(kr) in the r >> 1, m/r finite limit with l 2 m = k 2 − m 2 /r 2g(r, α, t) = ∑ B s m(r, t)e is ∫ l mdr−imα + (∗)Alan C. Newell, Zhiying Sun, Patrick D. Shipman<strong>Phyllotaxis</strong> <strong>and</strong> <strong>patterns</strong> on plants