Phyllotaxis, disk packing, and Fibonacci numbers
نویسندگان
چکیده
منابع مشابه
Fibonacci numbers in phyllotaxis : a simple model
A simple model is presented which explains the occurrence of high order Fibonacci number paras-tichies in asteracae flowers by two distinct steps. First low order parastichies result from the fact that a new floret, at its appearance is repelled by two former ones, then, in order to accommodate for the increase of the radius, parastichies numbers have to evolve and can do it only by applying th...
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The principal conclusion is that Fibonacci phyllotaxis follows as a mathematical necessity from the combination of an expanding apex and a suitable spacing mechanism for positioning new leaves. I have considered an inhibitory spacing mechanism at some length, as it is a plausible candidate. However, the same treatment would apply equally well to depletion of, or competition for, a compound by d...
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The energy E(G) of a graph G is the sum of the absolute values of the eigenvalues of G. In this article we consider the problem whether generalized Fibonacci constants $varphi_n$ $(ngeq 2)$ can be the energy of graphs. We show that $varphi_n$ cannot be the energy of graphs. Also we prove that all natural powers of $varphi_{2n}$ cannot be the energy of a matroid.
متن کاملDo Fibonacci numbers reveal the involvement of geometrical imperatives or biological interactions in phyllotaxis?
Complex biological patterns are often governed by simple mathematical rules. A favourite botanical example is the apparent relationship between phyllotaxis (i.e. the arrangements of leaf homologues such as foliage leaves and floral organs on shoot axes) and the intriguing Fibonacci number sequence (1, 2, 3, 5, 8, 13 . . .). It is frequently alleged that leaf primordia adopt Fibonacci-related pa...
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In 1985 Simion and Schmidt showed that the number of permutations in Sn which avoid 132, 213, and 123 is equal to the Fibonacci number Fn+1. We use generating function and bijective techniques to give other sets of pattern-avoiding permutations which can be enumerated in terms of Fibonacci or k-generalized Fibonacci numbers.
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ژورنال
عنوان ژورنال: Physical Review E
سال: 2017
ISSN: 2470-0045,2470-0053
DOI: 10.1103/physreve.95.022401