Phyllotactic patterns on plants

An approach to minimize the elastic energy of the plant surface posticts spiral and whorl patterns was described. The strain energy was minimized by configurations consiting of special triads of almost periodic deformations. It was found that when the stress was larger than critical value, the constant deformation state was found to be linearly unstable and certain shapes and configurations were amplified. A wide spectrum of plant patterns were reproduced with the divergence angles observed in nature, to show the occurrences of Fibonacci-like sequences and the golden angle as natural consequencies.