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LogGrowth - “D” and nonzero “T” Computer generated...

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The Golden Mean • Ratio of 1:.6180339…
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The Golden Mean in Architecture Zen Temple in Kyoto Stonehenge
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Logarithmic Spiral in nature: Nautilus pompilius
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Sunflower seeds
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Leonardo Fibonacci of Pisa -- ca 1170-1240 • Published Liber Abaci , 1202 • Introduced Arabic numerals, the concepts of zero, and positional notation to the West • Fibonacci series named after a problem presented in Liber Abaci: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144 . . .
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Fibonacci Series in plant growth
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Logarithmic spirals in Greek art
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Golden Mean in Greek Sculpture
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Seurat and the Golden Mean
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Musical intervals and the perception of harmony
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The cochlea: a logarithmic spiral
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The Fibonacci Series
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Foraminifera and the logarithmic spiral
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Dave Raup and the logarithmic spiral in molluscs
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Varying “D” in Nautilus euomphalus and N. pompilius
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Increasing “D” still further
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“D” : mathematical abstraction, or biological reality?
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Varying “W” and “T”
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Architectonica : nonzero “D” and “T” Volutid gastropod: zero
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Unformatted text preview: “D” and nonzero “T” Computer generated gastropods using W,D,T,S More computer generated molluscs Adaptation as deviation from logarithmic growth Archimedean spiral in trace fossils The “Raup Block” • Why are certain combinations of Raup parameters uncommon? Dimensionless Raup parameters: 4 suffice to describe any pure logarithmic shell shape • W: whorl expansion rate • D: distance from coiling axis • T: translation rate down coiling axis • S: shape of generating curve Varying W • Note extension past generating curve The problem of intersecting umbos in the Bivalvia • Inherent consequences of the mode of growth force deviation from logarithmic growth Genus Arca: an example of one solution to the “umbo problem” Inherent geometric constraints and uncoiled gastropods: the Precious Wenteltrap ( Epitoneum scalare ) • T = 2(W) .5 (W-1) The Raup Block Spiral nebula...
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