Visibility in a pure model of golden spiral phyllotaxis

Herrmann, Burghard

doi:10.1016/j.mbs.2018.05.003

Cited by 4 publications

(2 citation statements)

References 11 publications

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“…The spiral as one of the fundamental morphologies of the universe has been well adopted by the nature, specially by the plants, the leaves, florets, and seeds are well organized in repeated patterns in the forms of spirals. Phyllotaxis is the study about arrangement of the leaves, florets, and seeds on the stems and flower buds [1][2][3][4][5].…”

Section: Introductionmentioning

confidence: 99%

Morphological Simulation of Phyllotactic Spiral-Ring Patterns by the Galactic Spiral Equations from the ROTASE Model

Pan¹

2022

Preprint

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This short paper demonstrates that the galactic spiral equations developed from ROTASE model can be used to morphologically simulate the phyllotactic spiral-ring patterns of plants. It is also noticed during this project that although the numbers in the Fibonacci sequence dominate the phyllotactic numbers, there are still significant phyllotactic numbers are not in the Fibonacci sequence, however, most of those numbers are well fit into a Fibonacci sibling sequence starting with numbers 0 and 2. Many plants show the phyllotactic number pairs of 10-16, 16-26 and 26-42 from the Fibonacci sibling sequence, which is the second dominated sequence in the phyllotaxis.

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Section: Introductionmentioning

confidence: 99%

Morphological Simulation of Phyllotactic Spiral-Ring Patterns by the Galactic Spiral Equations from the ROTASE Model

Pan¹

2022

Preprint

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“…e golden ratio is also known as the golden section, golden proportion, and golden mean [1]. e golden ratio has been found incorporated almost in all natural or organic structures, such as the bone structure of human beings [2][3][4], the seed pattern and geometry of plants [5], the spiral of a sea shell [6], and spiral galaxy [7]. e golden ratio was found in art and architecture as it produces pleasing shapes [8], even in special relativity [9].…”

Section: Introductionmentioning

confidence: 99%

Shrinkage Points of Golden Rectangle, Fibonacci Spirals, and Golden Spirals

Duan

2019

Discrete Dynamics in Nature and Society

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We investigated the golden rectangle and the related Fibonacci spiral and golden spiral. The coordinates of the shrinkage points of a golden rectangle were derived. Properties of shrinkage points were discussed. Based on these properties, we conduct a comparison study for the Fibonacci spiral and golden spiral. Their similarities and differences were looked into by examining their polar coordinate equations, polar radii, arm-radius angles, and curvatures. The golden spiral has constant arm-radius angle and continuous curvature, while the Fibonacci spiral has cyclic varying arm-radius angle and discontinuous curvature.

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The Specified Three Distance Theorem

Herrmann

2020

The American Mathematical Monthly

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Visibility in a pure model of golden spiral phyllotaxis

Cited by 4 publications

References 11 publications

Morphological Simulation of Phyllotactic Spiral-Ring Patterns by the Galactic Spiral Equations from the ROTASE Model

Morphological Simulation of Phyllotactic Spiral-Ring Patterns by the Galactic Spiral Equations from the ROTASE Model

Shrinkage Points of Golden Rectangle, Fibonacci Spirals, and Golden Spirals

The Specified Three Distance Theorem

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