Chapter 8: Implications for Everyday Systems

Section 6: Growth of Plants and Animals

Projections of [phyllotaxis] patterns

The literature of phyllotaxis is full of baroque descriptions of the features of projections of patterns with golden ratio angles. In the pictures below, the nth point has position Sqrt[n]{Sin[#],Cos[#]}&[2π n GoldenRatio], and in such pictures regular spirals or parastichies emanating from the center are seen whenever points whose numbers differ by Fibonacci[m] are joined. Note that the tips of many growing stems seem to be approximately paraboloidal, making the nth point a distance Sqrt[n] from the center.

Projections of [phyllotaxis] patterns image 1

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