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…
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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
- 1991
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
- 1932
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.