Related papers: Phyllotactic structures in radially growing spatia…
The process of formation of fractal structure in one-dimensional self-gravitating system is examined numerically. It is clarified that structures created in small spatial scale grow up to larger scale through clustering of clusters, and…
Spatial patterns arising spontaneously due to internal processes are ubiquitous in nature, varying from regular patterns of dryland vegetation to complex structures of bacterial colonies. Many of these patterns can be explained in the…
Morphogenetic patterns are highly sophisticated dissipative structures. Are they governed by the same general mechanisms as chemical and hydrodynamic patterns? Turing's symmetry breaking and Wolpert's signalling provide alternative…
We report numerical investigations of a three-dimensional model of diffusive growth of fine particles, the internal structure of which corresponds to different crystal lattices. A growing cluster (particle) is immersed in, and exchanges…
We study the mechanisms of pattern formation for vegetation dynamics in water-limited regions. Our analysis is based on a set of two partial differential equations (PDEs) of reaction-diffusion type for the biomass and water and one ordinary…
The emergence of large scale structures in biological systems, and in particular the formation of lines of hierarchy, is observed in many scales, from collections of cells to groups of insects to herds of animals. Motivated by phenomena in…
The rapid and complex patterning of biosilica in diatom frustules is of great interest in nanotechnology, although it remains incompletely understood. Specific organic molecules, including long-chain polyamines, silaffins, and silacidins…
We propose a novel class of spirals that are based on perfect polygonal formations. The spirals are defined by a fractal of right triangles that delineate their geometry and determine their progression rates and modes. We show how these…
Cohesive particles form agglomerates that are usually very porous. Their geometry, particularly their fractal dimension, depends on the agglomeration process (diffusion-limited or ballistic growth by adding single particles or…
We identify a new type of pattern formation in spatially distributed active systems. We simulate one-dimensional two-component systems with predator-prey local interaction and pursuit-evasion taxis between the components. In a sufficiently…
We consider diffusion limited aggregation of particles of two different kinds. It is assumed that a particle of one kind may adhere only to another particle of the same kind. The particles aggregate on a linear substrate which consists of…
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…
The formation of vegetation patterns in the arid and the semi-arid climatic zones is studied. Threshold for the biomass of the perennial flora is shown to be a relevant factor, leading to a frozen disordered patterns in the arid zone. In…
The presence of spiral structure in isolated galaxies is a problem that has only been partially explained by theoretical models. Because the rate and pattern of star formation in the disk must depend only on mechanisms internal to the disk,…
A first-principles statistical theory is constructed for the evolution of two dimensional interfaces in Laplacian fields. The aim is to predict the pattern that the growth evolves into, whether it becomes fractal and if so the…
The biopolymers actin and microtubules are often in an ongoing assembling/disassembling state far from thermal equilibrium. Above a critical density this leads to spatially periodic patterns, as shown by a scaling argument and in terms of a…
In complex systems, groups of interacting objects may form prevalent and persistent spatiotemporal patterns, which we refer to as motifs. These motifs can exhibit features that reveal how individual objects interact with one another.…
We show that the process of spontaneous symmetry breaking can trap a field theoretic system in a highly non-trivial state containing a lattice of domain walls. In one large compact space dimension, a lattice is inevitably formed. In two…
Granulate physics has made considerable progress during the past decades in the understanding of static and dynamic properties of large ensembles of interacting macroscopic particles, including the modeling of phenomena like jamming,…
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…