Phyllotaxis is the spatial arrangement of leaves in blooms and was introduced in Sect. 3.4. Also, we previously discussed different procedures for the production of phyllotaxial patterns. In the following, a solution with L-systems is illustrated.
Golden Section ^ We will therefore return to the arrangement of the seeds in a sunflower, which was likewise addressed in Sect. 3.4. With a parametric L-system the typical angle of rotation is modeled according to the Golden Angle of 137.5° in combination with the square root increase of the radius (see also [66]). Thereby D is the L-system for the description of a small circle, and w = A(n):
A(n) ::= +(137.5)[/(^П) – D]A(n + 1).
Accordingly, a complete head of a sunflower can be generated, as shown in Fig. 5.9, with the aid of L-systems for the creation of the form of the seeds S, the inflorescence R, and the petals M, N, O, and P:
A(n) ::= +(137.5)[f^/n)C]A(n +1) C(n) : n < 440 ::= – S
The system differentiates the six forms to be produced according to “the control variable” n (in this case also an index). If the control variable is smaller than 440, seeds are produced, then inflorescences, and finally different forms of petals.
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Contrary to the sample models in Sect. 4.13, the L-system again is a descriptive model, which does not relate to natural processes, but only approximates the outer appearance of the corresponding object.
