Don Kaplan - his legacy: Influencing teaching and research
Cooke, Todd .
Fibonacci Numbers in Phyllotactic Patterns: Geometrical Imperative or Prosaic Consequence?.
It is frequently alleged that complex biological patterns are governed by simple mathematical rules. A botanical example often cited with unbridled enthusiasm is the apparent relationship between phyllotaxis (i.e., the arrangements of leaf homologues such as foliage leaves and floral organs) and the simple, but enigmatic Fibonacci number sequence (1,2,3,5,8,13...). The goals of this talk are: 1) to identify the fundamental properties of all number sequences; 2) to interpret the Fibonacci sequence with respect to these properties in order to illustrate its intrinsic limitations for describing all phyllotactic patterns; and 3) to evaluate whether or not the phyllotactic arrangements that are appropriately described with Fibonacci numbers represent the geometrical equivalent of optimal packing. It is concluded from the above considerations as well as from recent efforts devoted to physical modeling that phyllotactic patterns fitting Fibonacci-based descriptions do not arise from a universal geometrical imperative inherent in all inanimate and animate objects but rather they are generated as the consequence of the underlying biological interactions specifying leaf position.
1 - University of Maryland, Cell Biology and Molecular Genetics, College Park, Maryland, 20742, USA
Presentation Type: Symposium
Location: Ballroom 2 (Cliff Lodge)
Date: Tuesday, August 3rd, 2004
Time: 8:15 AM