Botanical phyllotaxis

The golden parameter is perhaps best known from botanical phyllotaxis and from its relationship to five-fold symmetry, as evidenced by trigonometric formulae such as ... 

Logarithmic spirals are widely used, especially in the engineering sciences and for botanical phyllotaxis to solve optimization problems. In the case of a distribution with multiple sub-maxima, the procedure consists in the variation of a divergence angle between adjacent maxima on the spiral until the optimal distribution is realized. 

The observation that the convergence of Z/N -> r promotes nuclear stability was interpreted to imply a packing mode for nucleons in three-dimensional analogy of botanical phyllotaxis. The general property, N >Z, of stable nuclides then results in a golden excess of x = Z — xN protons, which form an electrically... 

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