Constructing the sunflower head

Abstract By assigning the Fibonacci angle of 137.507… degrees between any two consecutive individual flowers (florets), and controlling the logarithmic scatter of the floral positions, one of us (Davis) has constructed the sunflower head, botanically known as the capitulum. A mathematical explanation for the configuration seen on the capitulum thus constructed, which simulates that of a natural sunflower head, has been offered by the first author. The formation of the individual florets on the capitulum which eventually causes the emergence of arcs or spirals on it, whose numbers invariably match with the terms of Fibonacci Sequence, can be explained thus: The florets are formed one at a time on the highly compressed stem which flattens out into the disc. The disc gets widened as more and more florets are differentiated, and the older ones move away from the growing point (centralmost region) and the younger ones get distributed around this central point. A flower primordium is differentiated on a side of the stem apex, and the subsequent florets are generated at a fast rate with a constant time-interval between any two consecutive individuals. As the flowers get differentiated, the tip of the meristematic axis rotates so much so that the older florets are seen to move away from the growing point in logarithmic spirals that approximate to an Archimedes' spiral. Moreover, among any two consecutive florets, the younger one starts differentiating from the axis when the older one is at an angle φ1, such that φ 1 (2π−φ 1 ) forms the golden ratio (0.618…). This process continues till the genetic material is finished and the flower head is fully programmed. With favorable environmental conditions, the individual flowers expand at a uniform rate over time along with the simultaneous expansion of the disc. It is shown mathematically that the above theory can explain all the properties of a sunflower head whether large or small.