Related papers: Phyllotaxis: a non conventional crystalline soluti…

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…

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…

We consider the evolution of the packing of disks (representing the position of buds) that are introduced at the top of a surface which has the form of a growing stem. They migrate downwards, while conforming to three principles, applied…

Phyllotaxis, the regular arrangement of leaves or other lateral organs in plants including pineapples, sunflowers and some cacti, has attracted scientific interest for centuries. More recently there has been interest in phyllotaxis within…

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…

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…

Many physical systems can be studied as collections of particles embedded in space, evolving through deterministic evolution equations. Natural questions arise concerning how to characterize these arrangements - are they ordered or…

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…

A routine crystallography technique, crystal structure analysis, is rarely performed in computational condensed matter research. The lack of methods to identify and characterize crystal structures reliably in particle simulation data…

Tubular crystals, two-dimensional lattices wrapped into cylindrical topologies, arise in many contexts, including botany and biofilaments, and in physical systems such as carbon nanotubes. The geometrical principles of botanical…

The kinetic mechanisms underlying bottom-up assembly of colloidal particles have been widely investigated in efforts to control crystallization pathways and to direct growth into targeted superstructures for applications including photonic…

The simulation of many-particle systems often requires the detailed knowledge of proximity relations to reduce computational complexity and to provide a basis for specific calculations. Here we describe the basic scheme of a simulator of…

Photosynthesis is vital for the survival of entire ecosystems on Earth. While light is fundamental to this process, excessive exposure can be detrimental to plant cells. Chloroplasts, the photosynthetic organelles, actively move in response…

A novel, protean, topological soliton has recently been shown to emerge in systems of repulsive particles in cylindrical geometries, whose statics is described by the number-theoretical objects of phyllotaxis. Here we present a minimal and…

Herein, fundamentals of topology and symmetry breaking are used to understand crystallization and geometrical frustration in topologically close-packed structures. This frames solidification from a new perspective that is unique from…

Plants often exhibit regular arrangements of seeds or leaves, known as phyllotaxis, and can famously exhibit Fibonacci spirals, as in sunflower heads or on pine cones. While there are many models which can reproduce spiral formation, the…

Higher-order Voronoi diagrams and Delaunay mosaics in polygonal metrics have only recently been studied, yet no tools exist for visualizing them. We introduce a tool that fills this gap, providing dynamic interactive software for…

The optimal transport problem has many applications in machine learning, physics, biology, economics, etc. Although its goal is very clear and mathematically well-defined, finding its optimal solution can be challenging for large datasets…

Physical systems are frequently modeled as sets of points in space, each representing the position of an atom, molecule, or mesoscale particle. As many properties of such systems depend on the underlying ordering of their constituent…

Confocal microscopy of fluorescent labeled particles has been used to study the dynamical and structural properties of colloidal and granular matter in real space. Localization algorithms allow for a fully automatized determination of the…