Phyllotaxis and patterns on plants

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Paradigms <strong>and</strong> Mechanisms: connections?Paradigms are rules for the placement of the newest primordiumgiven the positions of all previous primordia.cf. packing efficiencyMechanisms involve instabilities of uniform states, the decompositionof the phase space into active A <strong>and</strong> passive P(A) modes, thecoordinatization of A with (amplitude) order parameters, <strong>and</strong> orderparameter equations which may be gradient flows with a free energy.cf. energy minimizationHow to connect these ideas?Alan C. Newell, Zhiying Sun, Patrick D. Shipman<strong>Phyllotaxis</strong> <strong>and</strong> <strong>patterns</strong> on plants
Biochemical factorsReinhardt (2000) showed that hormone Auxin is instrumental ingrowth <strong>and</strong> uneven distribution of Auxin is the reason for theformation of phyllotaxisAlan C. Newell, Zhiying Sun, Patrick D. Shipman<strong>Phyllotaxis</strong> <strong>and</strong> <strong>patterns</strong> on plants
Page 1 and 2: Phyllotaxis <stron
Page 4 and 5: More Examples of Patterns on Plants
Page 6: Diagrams of phylla formationAlan C.
Page 9 and 10: Diagrams of phylla formationAlan C.
Page 11: Mechanisms and mod
Page 15 and 16: Biochemical factorsReinhardt (2000)
Page 17 and 18: Mechanical FactorsFvKD Equation(Des
Page 19 and 20: Patterns arising from the governing
Page 21 and 22: Amplitude Equations 1. EquationsLin
Page 23 and 24: OutcomeTheorem: The amplitude equat
Page 25 and 26: PDE SimulationFront propagating out
Page 45 and 46: PDE SimulationAlan C. Newell, Zhiyi
Page 47: TransitionsHow are transitions achi

Phyllotaxis and patterns on plants

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