#### Limited Bibliography

I. Adler, D. Barabé, and R. V. Jean (1997). A History
of the Study of Phyllotaxis, *Annals of Botany*, **80**,
231-244.

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 y**ou 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**,
178-312.

*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**,
229-241.

*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"
hypothesis. *

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
research page.*

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
Publishing.

*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**,
184-185.

*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*.