Related papers: Phyllotaxis, disk packing and Fibonacci numbers
One of humanity's earliest mathematical inquiries might have involved the geometric patterns in plants. The arrangement of leaves on a branch, seeds in a sunflower, and spines on a cactus exhibit repeated spirals, which appear with an…
Phyllotaxis describes the arrangement of florets, scales or leaves in composite flowers or plants (daisy, aster, sunflower, pinecone, pineapple). As a structure, it is a geometrical foam, the most homogeneous and densest covering of a large…
We propose an evolutionary mechanism of phyllotaxis, regular arrangement of leaves on a plant stem. It is shown that the phyllotactic pattern with the Fibonacci sequence has a selective advantage, for it involves the least number of…
Phyllotaxis, the search for the most homogeneous and dense organizations of small disks inside a large circular domain, was first developed to analyze arrangements of leaves or florets in plants. Then it has become an object of study not…
We have previously explored cylindrical packings of disks and their relation to sphere packings. Here we extend the analytical treatment of disk packings, analysing the rules for phyllotactic indices of related structures and the variation…
Phyllotactic patterns, i.e. regular arrangements of leaves or seeds around a plant stem, are fascinating examples of complex structures encountered in Nature. In botany, their symmetries develop when a new primordium periodically grows in…
The shape of the cross section of a dense fiber bundle is related to the symmetry of its molecular packing. However, this statement might be belied by type I collagen fibrils which have a rounded section of high symmetry while structural…
This paper investigates a model of plant organ placement motivated by the appearance of large Fibonacci numbers in phyllotaxis, and provides the first large-scale empirical validation of this model. Specifically it evaluates the ability of…
We demonstrate that the pattern forming partial differential equation derived from the auxin distribution model proposed by Meyerowitz, Traas and others gives rise to all spiral phyllotaxis properties observed on plants. We show how the…
We investigate the evolution of galactic disks in N-body Tree-SPH simulations. We find that disks, initially truncated at three scale-lengths, can triple their radial extent, solely driven by secular evolution. Both Type I (single…
The developing structure in systems of compacting ductile grains were studied experimentally in two and three dimensions. In both dimensions, the peaks of the radial distribution function were reduced, broadened, and shifted compared with…
Jean's `Fundamental Theorem of Phyllotaxis' (\emph{Phyllotaxis: a systematic study in Plant Morphogenesis}, CUP 1994) describes the relationship between the count numbers of observed spirals in cylindrical lattices and the horizontal angle…
We introduce and study properties of phyllotactic and rhombic tilings on the cylin- der. These are discrete sets of points that generalize cylindrical lattices. Rhombic tilings appear as periodic orbits of a discrete dynamical system S that…
In this review, I discuss just three aspects of the stability and evolution of galactic discs. (1) I first review our understanding of the bar instability and how it can be controlled. Disc galaxies in which the orbital speed does not…
A model of the regular arrangement of leaves on a plant stem (phyllotactic patterns) is proposed, based on a new plant pattern algorithm. Tripartite patterning is proposed to occur by the interaction of two signaling pathways. Each pathway…
Galaxy evolution is in transition from an early universe dominated by hierarchical clustering to a future dominated by secular processes. These result from interactions involving collective phenomena such as bars, oval disks, spiral…
Stars in disks of spiral galaxies are usually assumed to remain roughly at their birth radii. This assumption is built into decades of modelling of the evolution of stellar populations in our own Galaxy and in external systems. We present…
We seek to understand the origin of radial migration in spiral galaxies by analyzing in detail the structure and evolution of an idealized, isolated galactic disk. To understand the redistribution of stars, we characterize the…
We study iterations of two classical constructions, the evolutes and involutes of plane curves, and we describe the limiting behavior of both constructions on a class of smooth curves with singularities given by their support functions.…
The formation and evolution of disk galaxies in the cosmological context is studied. We consider the observable properties of disk galaxies and treat the disk formation and galactic evolutionary processes in a self-consistent fashion. We…