Chapter 8: Implications for Everyday Systems

Section 6: Growth of Plants and Animals

Implementation [of phyllotaxis model]

It is convenient to consider a line of discrete cells, much as in a continuous cellular automaton. With a concentrations list c, the position p of a new element is given by Position[c,Max[c],1,1][[1,1]], while the new list of concentrations is λ c+RotateRight[f,p] where f is a list of depletions associated with addition of a new element at position 1. In the main text a Gaussian form is used for f. Other smooth functions typically nevertheless yield identical results. Note that in order to get an accurate approximation to a golden ratio angle there must be a fairly large number of cells.

Image Source Notebooks:

From Stephen Wolfram: A New Kind of Science [citation]