Phyllotaxis and patterns on plants

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OutcomeTheorem: Under R → Rφ mn , φ mn = m+nφmφ+n = 1+φ22φ≃ φ − 1/2, theamplitude equations of two different Fibonacci sequences areisomorphic <strong>and</strong> in particular,E(1, 2, 3, 5, 8, ...; R) = E(1, 3, 4, 7, ...; 1.17R)1,3,4,7,...Alan C. Newell, Zhiying Sun, Patrick D. Shipman<strong>Phyllotaxis</strong> <strong>and</strong> <strong>patterns</strong> on plants
TransitionsHow are transitions achieved between whorls <strong>and</strong> Fibonaccisequences <strong>and</strong> between different Fibonacci sequences?e.g. 2,2,4 → 2,3,5e.g. 1,2,3,5, 8 → 1,3,4,7,..cf. Eckhaus, skew-varicose instabilitiesAlan 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 and 12: Mechanisms and mod
Page 13 and 14: Biochemical factorsReinhardt (2000)
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: PDE SimulationAlan C. Newell, Zhiyi

Phyllotaxis and patterns on plants

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