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 (√n{Sin[#], Cos[#]} &)[2π n GoldenRatio]
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(\!\(\*SqrtBox[\(n\)]\){Sin[#],Cos[#]}&)[2\[Pi]n GoldenRatio]
, and in such pictures regular spirals or parastichies emanating from the center are seen whenever points whose numbers differ by Fibonacci[m]
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Fibonacci[m]
are joined. Note that the tips of many growing stems seem to be approximately paraboloidal, making the nth point a distance √n
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\!\(\*SqrtBox[\(n\)]\)
from the center.
![Projections of [phyllotaxis] patterns image 1](/nks/img/inline/page1007a.png)