Sister is asking because she stumbled across this abstract and would dearly like to read the full paper. If anyone has access and could get it Sister would be very very grateful. Lately she has been spending a lot of time looking into lifeforms that mimic the fundamental energy pattern. Like the ones you see when you look at a pine cone from the bottom end, similar to crop patterns and other sacred geometry.
This is what Sister is after if anyone can swing it. Thanks in advance.
Journal of Theoretical Biology
Polygonal planforms and phyllotaxis on plants
P.D. Shipman, , A.C. Newell
Department of Mathematics, University of Arizona, Tucson, AZ 85721, USA
Received 18 October 2004. Revised 19 January 2005. Accepted 2 March 2005. Available online 18 April 2005.
Abstract
We demonstrate how phyllotaxis (the arrangement of leaves on plants) and the ribbed, hexagonal, or parallelogram planforms on plants can be understood as the energy-minimizing buckling pattern of a compressed sheet (the plant's tunica) on an elastic foundation. The key idea is that the elastic energy is minimized by configurations consisting of special triads of periodic deformations. We study the conditions that lead to continuous or discontinuous transitions between patterns, state testable predictions, and suggest experiments to test the theory.
This is what Sister is after if anyone can swing it. Thanks in advance.
Journal of Theoretical Biology
Polygonal planforms and phyllotaxis on plants
P.D. Shipman, , A.C. Newell
Department of Mathematics, University of Arizona, Tucson, AZ 85721, USA
Received 18 October 2004. Revised 19 January 2005. Accepted 2 March 2005. Available online 18 April 2005.
Abstract
We demonstrate how phyllotaxis (the arrangement of leaves on plants) and the ribbed, hexagonal, or parallelogram planforms on plants can be understood as the energy-minimizing buckling pattern of a compressed sheet (the plant's tunica) on an elastic foundation. The key idea is that the elastic energy is minimized by configurations consisting of special triads of periodic deformations. We study the conditions that lead to continuous or discontinuous transitions between patterns, state testable predictions, and suggest experiments to test the theory.
