This is a question that fascinated Alan Turing, who wrote a classic paper called "The Chemical Basis of Morphogenesis" and other unfinished papers about the subject (some published in a book called "Morphogenesis"). He used lots of heavy math that came so naturally to him, to model plant growth as a reaction-diffusion system running in a ring of cells (the stem of the plant). By computing the reactions by hand on paper, he studied how cells could grow into "parastichy" with spiral patterns related by Fibbonachi numbers. http://botanydictionary.org/parastichy.html http://www.dna.caltech.edu/courses/cs191/paperscs191/turing....