hunh: the Delaunay triangulation for the phyllotaxis pattern has well defined annular discontiguities in grainpic.twitter.com/JHGvJgr889
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Indeed it looks like it! Here are circles with radii as powers of phi overlaidpic.twitter.com/82DAW2yQRv
Maybe there's a connection to Lucas? For n>1, the Lucas number L_n is the closest integer to φ^n (and the distance between the two decreases exponentially with n). [The Lucas numbers are defined by L_0=2, L_1=1, and the Fibonacci relation (each is the sum of the previous two).]
At any given radius, there is a sequence of three Fibonacci numbers that give the offset to a node's three nearest neighbors. Long long ago I worked out the radii at which this sequence shifts; they are indeed related by the golden ratio if memory serves.
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