I. Adler, D. Barabé, and R. V. Jean (1997). A History
of the Study of Phyllotaxis, Annals of Botany, 80,
P. Atela, The Geometric and Dynamic Essence of Phyllotaxis, Math. Model. Nat. Phenom.
Vol. 6, No. 2, 2011, pp. 173–186
Generating Fibonacci phyllotaxis by stacking disks on a cone.
P. Atela, C. Golé, and S. Hotton (2002). A
Dynamical System for Plant Pattern Formation: Rigorous Analysis (P. Atela, C. Golé, S. Hotton, J.
Nonlinear Sci. Vol. 12, Number 6
See the description in the
research page, where you can find preprints describing other models as well.
Barabé and Jean (Eds.) (1998). Symmetry in Plants,
World Scientific Publishing.
A compilation of surveys of the most
recent research by dozens of scientists, in all the fields pertaining
to phyllotaxis, written by the scientists themselves.
S. Douady and Y. Couder (1996). Phyllotaxis as a Dynamical Self
Organizing Process (Part I, II, III), J. theor. Biol. 139,
Groundbreaking articles introducing the
models that are at the center of our research.
Dumais, J. and Kwiatkowska, D. (2002). Analysis of surface growth
in shoot apices. The Plant Journal 31,
Develops a promising technique of 3-D
analysis of growing plant meristems, using a non destructive microscopy
method as well as curvature analysis at the cellular level.
Dumais, J. and C.R. Steele (2000). New evidence for the role
of mechanical forces in the shoot apical meristem, Journal
of Plant Growth Regulation 19, 7-18.
Uses stress analysis of incisions of
the growing head of sunflower as supporting evidence for buckling.
L.H. Hernandez and Paul B. Green (1993). Transduction for the
expression of structural patterns: analysis in sunflower, The
Plant Cell, Vol 5, 1725-1738.
A comparative analysis of various proposed
physiological mechanisms for phyllotaxis, favouring the "buckling"
S. Hotton, V. Johnson, J. Wilbarger, K. Zwieniecki, P. Atela, C. Golé, J. Dumais (2006) The possible and the actual in phyllotaxis: Bridging the gap between empirical observations and iterative models. Journal of Plant Growth Regulation 25: 313-323 (pdf .7 MB)
This paper presents new methods for the geometrical analysis of phyllotactic patterns and their comparison with patterns produced by simple, discrete dynamical systems.
S. Hotton (1999). Symmetry of Plants, Ph.D. Thesis,
UC Santa Cruz.
See the description in the
Jean, Roger V. (1994). Phyllotaxis: A systemic study in plant
morphogenesis. Cambridge University Press: Cambridge.
A comprehensive look at many mathematical
models of phyllotaxis.
L.S. Levitov (1991): Energetic Approach to Phyllotaxis, Europhys.
Lett., 14 (6), 533-539.
An inspiring article on the use of (hyperbolic)
symmetry in phyllotaxis. See also the related article in "Symmetry
in Plants" by Levitov and Lee.
R.D. Meicenheimer (1998). Decussate to spiral transitions in
phyllotaxis, in Symmetry in Plants, World Scientific
Correlates changes of the eccentricity
of the meristem to decussate to spiral transitions. Gives relative
frequencies of different phyllotactic patterns.
D. Reinhardt, T. Mandel, and C. Kuhlemeier (2000).
Auxin Regulates the Initiation and Radial Position of Plant Lateral
Organs, The Plant Cell, Vol. 12, 507–518
The title says it. This gives credence
to a biochemically driven type of model for the inception of primordia.
R. S. Smith, S. Guyomarc'h,T. Mandel, D. Reinhardt, C. Kuhlemeier, and P. Prusinkiewicz (2005) A plausible model of phyllotaxis, Proc. Nat. Acad. Sc., Vol 103, issue 5
Builds a comprehensive computer/mathematical model based on many of the auxin transport mechanisms observed. Obtain Fibonacci phyllotaxis with added, reasonable assumptions.
R. Rutishauser (1998). Parameters of a quantitative
Phyllotaxis Analysis, in Symmetry in Plants, World
Scientific Publishers, 171-212.
Gives a table of
measurements of many plants samples ( plastochrone
ratios, divergence angles, leaf arc, phyllotactic type and others).
M. Snow and R. Snow (1951). On the question of tissue
tensions in stem apices. New Phytologist 50,
phyllotactic type and others).
Turing, A.M.(1952): The chemical basis of morphogenesis.
Phil. Trans. R.Soc. London B139, 545-566
Seminal paper showing mathematically
that certain chemical reactions can lead to non-homogeneous concentrations
of chemicals - hence patterning. [Turing was a father figure in
the birth of computers]. Turing also spent some time thinking specifically about phyllotaxis. See his unpublished manuscripts on the subject.