Phyllotaxis spirals can be generated mathematically from Fibonacci ratios : the Fibonacci sequence runs 1, 1, 2, 3, 5, 8, 13 . . . ( each subsequent number being the sum of the two preceding ones ).
22.
In 2012, Adler contributed to a family venture when he wrote the foreword for his then 99-year-old father's 87th book, " Solving the Riddle of Phyllotaxis : Why the Fibonacci Numbers and the Golden Ratio Occur on Plants ".
23.
The album cover features a phyllotaxis spiral, a natural formation occurring in some plants, which Letchford described as a multitude of elements forming their own collective-and the inspiration for the album's title, as the band very often take inspiration from nature.
24.
The leaves are generally flat with a decurrent base and a spreading blade, but leading and cone-bearing shoots may also have small appressed scale-like leaves . The base phyllotaxis or leaf arrangement is spiral though the leaves usually form subopposite and nearly decussate pairs.
25.
They also appear in biological settings, such as branching in trees, phyllotaxis ( the arrangement of leaves on a stem ), the fruit sprouts of a pineapple, the flowering of an artichoke, an uncurling fern and the arrangement of a pine cone's bracts.
26.
Plant spirals can be seen in phyllotaxis, the arrangement of leaves on a stem, and in the arrangement ( parastichy ) of other parts as in snake fruit, as well as in the pattern of scales in pine cones, where multiple spirals run both clockwise and anticlockwise.
27.
The article references extensively an article by Vera W . de Spinadel ( for some reason linked to a top page, but the article in question is probably this one to cover the phyllotaxis sections, yet while that reference gives extensive coverage on Fibonacci numbers and metallic means, no mention at all is made of hyperbolic or Lucas functions.
28.
Some of the earliest ideas and mathematical descriptions on how physical processes and constraints affect biological growth, and hence natural patterns such as the spirals of phyllotaxis, were written by D'Arcy Wentworth Thompson in his 1917 book " On Growth and Form " and Alan Turing in his " The Chemical Basis of Morphogenesis " ( 1952 ).
29.
The book covers many topics including the effects of scale on the shape of animals and plants, large ones necessarily being relatively thick in shape; the effects of surface tension in shaping soap films and similar structures such as cells; the logarithmic spiral as seen in mollusc shells and ruminant horns; the arrangement of leaves and other plant parts ( phyllotaxis ); and Thompson's own method of transformations, showing the changes in shape of animal skulls and other structures on a Cartesian grid.
30.
:: The Phyllo-architect ( s ) believe that a concept-let's call it " Phyllotaxis in architecture ", say, is interesting, well-defined, and plainly discussed in numerous reliable sources such as ( . . . Le Corbusier . . . P for Thames Gateway . . . in Eden Project Arno Pronk Jerry Tate : Eden . . . P in Shadow Pavilion . . . P for Domes and indeed the seeming CoI source Phyllotaxy Towers by Saleh Masoumi.
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