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РЖ ВИНИТИ 34 (BI38) 96.05-04А3.20

Long, Charles A.
Leonardo da vinci's rule and fractal complexity in dichotomous trees [Text] / Charles A. Long // J. Theor. Biol. - 1994. - Vol. 167, N 2. - P107-113 . - ISSN 0022-5193
Перевод заглавия: Закон Леонародо да Винчи и фрактальная сложность дихотомических деревьев
Аннотация: A coincidence involving Leonardo da Vinci's ratios of branch diameters (0,707) in bifurcating trees and the limit of branch length ratios where fractal branching of bifurcating trees becomes non-fractal (at 0,707) suggests that constancy of the diameter ratios forces a fractal elaboration of the branch tips. The cylinder equation r{2}[2]/r{2}[1]=b[1]/2b[2] suggests and equality that does not occur in fact (because the b[2]/b[1] ratio is always smaller than da Vinci's ratio and further branching continues for fractal trees). The branching proliferates as a geometric progression. The resulting fractal complexity of the branch tips probably enhances the flow of fluids to and from leaves, creates a spacious bower, and lessens the crushing weight that would result from non-fractal branching. Tree growh upward is initially rapid but becomes regularly diminished by fractal elaboration. A hypothesis presented suggests the number of real branchings in some trees is limited by da Vinci's ratio. The old/(new + old) wood ratios converge to the original branch ratio meaning the dichotomous tree increases new wood by 2b[2] * old wood at each branching. The linear dimension of the canopy (compared to the sum of the old and the end branches) also approaches the 0,707 constant at about five orders of branching, and if exceeding those orders there would seem to be adverse effects. США, Dep. of Biology, Univ. of Wisconsin, Stevens Point, WI 54481. Ил. 3. Библ. 13

ГРНТИ	34.55.15

ВИНИТИ 341.55.15.27
Рубрики: МАТЕМАТИЧЕСКИЕ МОДЕЛИ
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