Ideal phyllotaxis on general surfaces of revolution

Ridley, J. N.

doi:10.1016/0025-5564(86)90013-1

Cited by 21 publications

(13 citation statements)

References 4 publications

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“…Further recurrences are observed at Mo (10,11,12,13) Ru (10,11,12,13) 26 30 34 38 42 46 50 54 58 62 66 70 74 78 82 80 76 72 68 64 60 56 52 48 44 40 36 Cd (14,15,16,17) Ba (22,23,24,25) Nd (22,23,24,25) Gd (26,27,28,29) Yb (30,31,32,33) Hg (38,39,40,41) The total of 11 observed recurrences does not necessarily define the 11 expected periods. The consecutive Mo and Ru recurrences, for instance, only show that none of the four sequences has been interrupted between these two elements by the generation of some radioactive nuclide.…”

Section: Nuclidic Periodicitymentioning

confidence: 99%

“…The mechanism leading to the appearance of Fibonacci numbers is well known [26] and accepted: successive leaves appear on the stem at an angle of about 137.5 • (360/Φ 2 ), the golden section of the unit circle, which is between 3/8 and 2/5 of a revolution. Thus five leaves make up just under two revolutions and eight leaves just over three revolutions.…”

Section: Phyllotaxis and Growthmentioning

confidence: 99%

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Number Theory and the Periodicity of Matter

Boeyens

Levendis

2008

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Section: Nuclidic Periodicitymentioning

confidence: 99%

Section: Phyllotaxis and Growthmentioning

confidence: 99%

Number Theory and the Periodicity of Matter

Boeyens

Levendis

2008

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“…Lintermann and Deussen proposed a similar approximation to derive a formula for placing organs on the surface of a sphere [19]. Both approaches are subsumed by the model of Ridley [31], which operates on arbitrary surfaces of revolution. Our algorithm is based on Ridley's analysis.…”

Section: Compact Phyllotactic Patternsmentioning

confidence: 99%

The use of positional information in the modeling of plants

Prusinkiewicz

Mündermann

Karwowski

et al. 2001

Proceedings of the 28th Annual Conference on Computer Graphics and Interactive Techniques

209

158

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We integrate into plant models three elements of plant representation identified as important by artists: posture (manifested in curved stems and elongated leaves), gradual variation of features, and the progression of the drawing process from overall silhouette to local details. The resulting algorithms increase the visual realism of plant models by offering an intuitive control over plant form and supporting an interactive modeling process. The algorithms are united by the concept of expressing local attributes of plant architecture as functions of their location along the stems.Keywords: realistic image synthesis, interactive procedural modeling, plant, positional information, phyllotaxis, Chomsky grammar, L−system, differential turtle geometry, generalized cylinder. Reference The use of positional information in the modeling of plants AbstractWe integrate into plant models three elements of plant representation identified as important by artists: posture (manifested in curved stems and elongated leaves), gradual variation of features, and the progression of the drawing process from overall silhouette to local details. The resulting algorithms increase the visual realism of plant models by offering an intuitive control over plant form and supporting an interactive modeling process. The algorithms are united by the concept of expressing local attributes of plant architecture as functions of their location along the stems.

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“…They argued that the most common angle turn between consecutive elements along this spiral in plants is the golden angle. The latter provides optimum packing [58,59], maximizing the exposure to light, rain and insects for pollination [46]. Structures in cells and viruses also follow this pattern [20].…”

Section: Lattice Historymentioning

confidence: 96%

Measurement of Areas on a Sphere Using Fibonacci and Latitude–Longitude Lattices

2009

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The area of a spherical region can be easily measured by considering which sampling points of a lattice are located inside or outside the region. This point-counting technique is frequently used for measuring the Earth coverage of satellite constellations, employing a latitude-longitude lattice. This paper analyzes the numerical errors of such measurements, and shows that they could be greatly reduced if the Fibonacci lattice were used instead. The latter is a mathematical idealization of natural patterns with optimal packing, where the area represented by each point is almost identical. Using the Fibonacci lattice would reduce the root mean squared error by at least 40%. If, as is commonly the case, around a million lattice points are used, the maximum error would be an order of magnitude smaller.

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Ideal phyllotaxis on general surfaces of revolution

Cited by 21 publications

References 4 publications

Number Theory and the Periodicity of Matter

Number Theory and the Periodicity of Matter

The use of positional information in the modeling of plants

Measurement of Areas on a Sphere Using Fibonacci and Latitude–Longitude Lattices

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