Phyllotaxis spiral

Figure 8-12. (a) The scattered leaf arrangement (phyllotaxis) of Plantago media (drawing by Ferenc Lantos, Pecs). Fibonacci numbers of spirals in the patterns of (b) Scales of a pinecone and (c) A cactus in Hawaii (b and c, photographs by the authors). 

Phyllotaxy.—Phyllotaxy is the study of leaf arrangement upon the stem or branch, and this may be either alternate, opposite, whorled, or verticillate, or fascicled. It is a general law in the arrangement of leaves and of all other plant appendages that they are spirally disposed, or on a line which winds around the axis like the thread of a screw. The spiral line is formed by the union of... 

P phyllotaxis/merism unordered I I spiral I trimerous I dimerous polymerous t.V.Wj uncertain I equivocal... 

Ihe character for number of perianth whorls (Fig 4. IB) is not strictly applicable in flowers with spiral phyllotaxis, but we have treated the number of so-called series of... 

Contrary to earlier beliefs, floral phyllotaxis patterns are very flexible. The direction is not only from spiral to whorled, but there was repeated evolution of spiral phyllotaxis from whorled in the perianth in basal angiosperms (Endress and Doyle, 2007, 2009 Doyle and Endress, 2011) and there is much evolutionary flexibility of patterns within families, genera or even species (Endress, 1987 Staedler and Endress, 2009). 

Leaves with spiral phyllotaxis (versus opposite in Zygophyllaceae El Hadidi, 1975 Liu and Zhou, 2008)... 

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. 

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