# Phyllotaxis as a Dynamical Self Organizing Process Part II: The Spontaneous Formation of a Periodicity and the Coexistence of Spiral and Whorled Patterns

@article{Douady1996PhyllotaxisAA, title={Phyllotaxis as a Dynamical Self Organizing Process Part II: The Spontaneous Formation of a Periodicity and the Coexistence of Spiral and Whorled Patterns}, author={St{\'e}phane Douady and Yves Couder}, journal={Journal of Theoretical Biology}, year={1996}, volume={178}, pages={275-294} }

Abstract The conditions for the appearance of a new primordium put forward by Snow & Snow (1952) are shown to form the rules of a dynamical iterative system more general than that based on Hofmeister's hypotheses (1868). This system is simple, generic and compatible with several of the ideas about the possible nature of the interaction between primordia. By numerical simulation, it is demonstrated that this system is sufficient to spontaneously generate time periodic regimes in which the…

## 117 Citations

Emergence of complex patterns in a higher-dimensional phyllotactic system

- Physics
- 2016

A hypothesis commonly known as Hofmeister’s rule states that primordia appearing at the apical ring of a plant shoot in periodic time steps are formed in the position where the most space is…

Multidimensional generalization of phyllotaxis

- Physics
- 2019

The regular spiral arrangement of various parts of biological objects (leaves, florets, etc.), known as phyllotaxis, could not find an explanation during several centuries. Some quantitative…

Fibonacci or quasi-symmetric phyllotaxis. Part I: why?

- Mathematics
- 2016

The study of phyllotaxis has focused on seeking explanations for the occurrence of consecutive Fibonacci numbers in the number of helices paving the stems of plants in the two opposite directions.…

A Dynamical System for Plant Pattern Formation: A Rigorous Analysis

- MathematicsJ. Nonlinear Sci.
- 2003

A rigorous mathematical analysis of a discrete dynamical system modeling plant pattern formation based on the work of physicists Douady and Couder, where fixed points are the spiral or helical lattices often occurring in plants.

Self-similarity and scaling in two models of phyllotaxis and the selection of asymptotic divergence angles.

- BiologyJournal of theoretical biology
- 2012

Noise and Robustness in Phyllotaxis

- BiologyPLoS Comput. Biol.
- 2012

This work incorporated stochasticity in the model and found three main classes of defects in spiral phyllotaxis – the reversal of the handedness of spirals, the concomitant initiation of organs and the occurrence of distichous angles – and investigated whether a secondary inhibitory field filters out defects.

Phyllotactic Patterns: A Biophysical Mechanism for their Origin

- Biology
- 1996

It is shown here that an initial undulating periodic pattern can arise in a flat unstructured annulus and proposed that at the moment of periodic pattern initiation the plant tissue simply manifests the spontaneous but complex properties of a two-layered inanimate sheet.

Phyllotaxis as an example of the symbiosis of mechanical forces and biochemical processes in living tissue

- BiologyPlant signaling & behavior
- 2008

The goals in this Addendum are to give a brief overview of current thinking on possible mechanisms for primordia (the bumps on the plant surface which eventually mature into fully developed structures such as leaves or florets) formation and give a descriptive narrative of the mathematical models which encode various hypotheses.

## References

SHOWING 1-10 OF 31 REFERENCES

PHYLLOTAXIS AS A DYNAMICAL SELF ORGANIZING PROCESS. PART I: THE SPIRAL MODES RESULTING FROM TIME-PERIODIC ITERATIONS

- Materials Science
- 1996

Abstract This article is the first of a series of three in which the various phyllotaxic modes are shown to result from successive iterations of two possible simple dynamical systems. In this first…

Phyllotaxis as a physical self-organized growth process.

- PhysicsPhysical review letters
- 1992

A specific crystalline order, involving the Fibonacci series, had until now only been observed in plants (phyllotaxis). Here, these patterns are obtained both in a physics laboratory experiment and…

Phyllotaxis and the Fibonacci Series

- MathematicsScience
- 1977

The principal conclusion is that Fibonacci phyllotaxis follows as a mathematical necessity from the combination of an expanding apex and a suitable spacing mechanism for positioning new leaves. I…

Energetic Approach to Phyllotaxis

- Mathematics
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Soft lattices subjected to strong compression are studied. Their equilibrium states form a hierarchical system of quasi-bifurcations. Underlying SL(2, Z) ⊗ Z2 symmetry of the problem is revealed. The…

Experiments on Phyllotaxis. II. The Effect of Displacing a Primordium

- Medicine
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In the present experiments a slight vertical cut was made in a radial plane through the area from which the next primordium was due to arise, or in other words through the presumptive area of Ix, a conclusion which strongly supports v a n It e r so n ’s theory of phyllotaxis (1907).

Experiments on Phyllotaxis. I. The Effect of Isolating a Primordium

- Mathematics
- 1932

Theories concerning the causes of phyllotaxis may be divided conveniently into two groups: that of SCHIMPER and BRAUN, who suggested that spiral sequences were due to a spiral growth impulse which travelled up the stem, the leaves arising at regular intervals along the course of this spiral.

A theory of the regulation of phyllotaxis based on Lupinus albus

- Environmental SciencePhilosophical Transactions of the Royal Society of London. Series B, Biological Sciences
- 1962

It is claimed that the theory provides an escape from the chief difficulty confronting a space-filling interpretation of phyllotaxis, and that this gradually regulates a disturbed system.

Models of biological pattern formation: common mechanism in plant and animal development.

- BiologyThe International journal of developmental biology
- 1996

It is concluded that the generation of complex structures in distantly related organisms may be based on similar mechanisms.

Phyllotaxis: Its quantitative expression and relation to growth in the apex

- BiologyPhilosophical Transactions of the Royal Society of London. Series B, Biological Sciences
- 1951

It is concluded that the numerical measures employed do not characterize solely the arrangement or positioning of the primordia, but are partially determined also by primordial shape, and a method of phyllotaxis assessment is proposed that is free from this ambiguity.