Self-organized Patterns Research Articles

Recognition of ecological vegetation fairy circles in intertidal salt marshes from UAV LiDAR point clouds

• Fairy circles are detected from 3D point clouds of UAV LiDAR for the first time. • A new model is proposed to correct the intensity data of UAV LiDAR. • Merely corrected intensity data can reliably be used for point cloud filtering. • Absent instantaneous UAV LiDAR scanning distances and scan angles are recovered. • The proposed method is promising for spatial patterns recognition in other scenes. Fairy circles (FC) are a type of spatial self-organized patterns that widely exist in various vegetation ecosystems and the accurate detection and quantitative characterization of these mysterious circles remain a technical challenge. In this study, vegetation FC in intertidal salt marshes are recognized from the derived reflectance information (backscattered intensity) and geometric quantities of light detection and ranging (LiDAR) carried on unmanned aerial vehicle (UAV). The specular effect on the UAV LiDAR intensity data over nadir regions of wet salt marshes is eliminated using the laser radar equation and Phong model where the absent distances and incidence angles are approximately retrieved on the basis of geometric and temporal relations in data collection. The FC are progressively recovered through three interconnected procedures. First, the retrieved reflectance information is used to discriminate the mudflat and vegetation points. Second, a spatial connectivity clustering algorithm is utilized on the extracted vegetation points to form individual spatially disconnected clusters. Finally, FC and regular vegetation are successfully recognized by jointly using the salient, size, and circularity features of the generated clusters. A multi-echo UAV LiDAR system is used for data collection at an intertidal salt marsh to assess the feasibility and prospects of the proposed method. Taking the manual detection results from the orthophoto generated by images of a UAV camera system as a reference, the missing detection rate, false detection rate, and area detection error of the proposed method are 6%, 9%, and 5%, respectively. Results suggest that UAV LiDAR is an extremely promising technique to characterize the geometric properties (e.g., location, size, and quantity) of FC from a holistic perspective.

Macroscopic and microscopic dynamics of a pedestrian cross-flow: Part II, modelling

In this work, we try to reproduce empirical results concerning the behaviour of a human crowd in a cross-flow using a hierarchy of models, which differ in the details of the body shape (using a disk-shaped body vs a more realistic elliptical shape) and in how collision avoiding is performed (using only information regarding “centre of mass” distance and velocity, or actually introducing body shape information). We verified that the most detailed model (i.e., using body shape information and an elliptical body) outperforms in a significant way the simplest one (using only centre of mass distance and velocity, and disk-shaped bodies). Furthermore, we observed that if elliptical bodies are introduced without introducing such information in collision avoidance, the performance of the model is relatively poor. Nevertheless, the difference between the different models is relevant only in describing the “tails” of the observable distributions, suggesting that the more complex models could be of practical use only in the description of high density settings. Although we did not calibrate our model in order to reproduce “stripe formation” self-organising patterns observed in the crossing area, we verified that they emerge naturally in all models.

Macroscopic and microscopic dynamics of a pedestrian cross-flow: Part I, experimental analysis

In this work we investigate the behaviour of a human crowd in a cross-flow by analysing the results of a set of controlled experiments in which subjects were divided into two groups, organised in such a way to explore different density settings, and asked to walk through the crossing area. We study the results of the experiment by defining and investigating a few macroscopic and microscopic observables. Along with analysing traditional indicators such as density and velocity, whose dynamics was, to the extent of our knowledge, poorly understood for this setting, we pay particular attention to walking and body orientation, studying how these microscopic observables are influenced by density. Furthermore, we report a preliminary but quantitative analysis on the emergence of self-organising patterns (stripes) in the crossing area, a phenomenon that had been previously qualitatively reported for human crowds, and reproduced in models, but whose quantitative analysis with respect to density conditions is, again according to our knowledge, a novel contribution.

Cellular automata approach to modeling self-organized periodic patterns in nanoparticle-doped liquid crystals.

Elementary cellular automata provide one of the simplest ways to generally describe the phenomena of pattern formation. However, they are considered too simple to be able to describe in detail the more complex phenomena occurring in real experimental systems. In this article, we demonstrate the an application of these methods to optical systems, providing an understanding of the mechanisms behind the formation of periodic patterns in nanoparticle-doped liquid crystals. Our extremely simplified model also explains the observed linear relationship between periodicity and system size.

Cellular reaction gene regulation network for swarm robots with pattern formation maneuvering control.

Self-organized pattern formation enables swarm robots to interact with local environments to self-organize into intricate structures generated by gene regulatory network (GRN) control methods without global knowledge. Previous studies have reported that it is challenging to maintain pattern formation stability during maneuvering in the environment due to local morphogenetic reaction rules. Motivated by the mechanism of the GRN in multi-cellular organisms, we propose a novel cellular reaction gene regulatory network (CR-GRN) for pattern formation maneuvering control. In CR-GRN, a cellular reaction network is creatively proposed to depict the robots, environment, virtual target pattern, and their interaction to generate emergent swarm behavior in multi-robot systems. A novel diffusion equation is proposed to simulate the process of morphogen diffusion among cells to ensure stable adaptive pattern generation. In addition, genes, proteins, and morphogens are used to define the internal and external states of cells and form a feedback regulation network. Simulation experiments are conducted to validate the proposed method. The results show that the CR-GRN can satisfy the requirements of turning curvature and maintain the robot's uniformity based on the proposed algorithm. This proves that robots using the CR-GRN can cooperate more effectively to cope in a complicated environment, and maintain a stable formation during maneuvering.

Synergetic synchronized oscillation by distributed neural integrators to induce dynamic equilibrium in energy dissipation systems

The synchronization phenomenon is common to many natural mechanical systems. Joint friction and damping in humans and animals are associated with energy dissipation. A coupled oscillator model is conventionally used to manage multiple joint torque generations to form a limit cycle in an energy dissipation system. The coupling term design and the frequency and phase settings become issues when selecting the oscillator model. The relative coupling relationship between oscillators needs to be predefined for unknown dynamics systems, which is quite challenging problem. We present a simple distributed neural integrators method to induce the limit cycle in unknown energy dissipation systems without using a coupled oscillator. The results demonstrate that synergetic synchronized oscillation could be produced that adapts to different physical environments. Finding the balanced energy injection by neural inputs to form dynamic equilibrium is not a trivial problem, when the dynamics information is not priorly known. The proposed method realized self-organized pattern generation to induce the dynamic equilibrium for different mechanical systems. The oscillation was managed without using the explicit phase or frequency knowledge. However, phase, frequency, and amplitude modulation emerged to form an efficient synchronized limit cycle. This type of distributed neural integrator can be used as a source for regulating multi-joint coordination to induce synergetic oscillations in natural mechanical systems.

Effect of the Polarity of Solvents on Periodic Precipitation: Formation of Hierarchical Revert Liesegang Patterns.

Liesegang pattern (LP) is one example of self-organized periodic precipitation patterns in nonequilibrium systems. Several studies have demonstrated that the LP morphology can track physicochemical environmental conditions (e.g., temperature); however, the polarity effect has not been explored to date. In this study, a copper chromate system is used to reveal the impact of solvent polarity on the evolving LP structure using water/organic solvent mixtures. In the typical case of using water/dimethyl sulfoxide (DMSO) mixtures, two drastic changes in LP morphology with increasing DMSO contents were found: (i) increasing frequency of the original structure and (ii) formation of a hierarchical pattern with the appearance of another, lower-frequency structure. Furthermore, the simulation model operating with a bimodal size distribution, allowing both homogeneous and heterogeneous precipitations showed good agreement with the experimental results. Therefore, this study demonstrated that LP can be tailored by solvent polarity and can be used for designing hierarchical precipitation patterns in a straightforward manner.

Cell shape anisotropy contributes to self-organized feather pattern fidelity in birds.

Developing tissues can self-organize into a variety of patterned structures through the stabilization of stochastic fluctuations in their molecular and cellular properties. While molecular factors and cell dynamics contributing to self-organization have been identified in vivo, events channeling self-organized systems such that they achieve stable pattern outcomes remain unknown. Here, we described natural variation in the fidelity of self-organized arrays formed by feather follicle precursors in bird embryos. By surveying skin cells prior to and during tissue self-organization and performing species-specific ex vivo drug treatments and mechanical stress tests, we demonstrated that pattern fidelity depends on the initial amplitude of cell anisotropy in regions of the developing dermis competent to produce a pattern. Using live imaging, we showed that cell shape anisotropy is associated with a limited increase in cell motility for sharp and precisely located primordia formation, and thus, proper pattern geometry. These results evidence a mechanism through which initial tissue properties ensure stability in self-organization and thus, reproducible pattern production.

Chemistry-Inspired Pattern Formation With Robotic Swarms

Self-organized emergent patterns can be widely seen in particle interactions producing complex structures such as chemical elements and molecules. Inspired by these interactions, this work presents a novel stochastic approach that allows a swarm of heterogeneous robots to create emergent patterns in a completely decentralized fashion and relying only on local information. Our approach consists of modeling the swarm configuration as a dynamic <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Gibbs Random Field</i> (GRF) and setting constraints on the neighborhood system inspired by chemistry rules that dictate binding polarity between particles. Using the GRF model, we determine velocities for each robot, resulting in behaviors that lead to the creation of patterns or shapes. Simulated experiments show the versatility of the approach in producing a variety of patterns, and experiments with a group of physical robots show the feasibility in potential applications.

Denken uit gewoonten: een belichaamd perspectief

Thinking out of habit: an embodied perspective In the second half of the twentieth century, habit had received little attention in the cognitive sciences and philosophy of cognition. This despite the extensive theoretical attention habit received in phenomenology and pragmatism. This is because due to influence of behaviorism and the cognitivist revolution, habit was reduced to mechanical stimulus-response reaction that is learned through drill and repetition, and therefore habit cannot be considered intelligent. In this article I argue that a richer and more accurate notion of habit is possible through an embodied vision of cognition, namely enactivism and ecological psychology. This means that we can consider habit as intelligent without equating habit with reflective thought. Such a notion is possible because both enactivism and ecological psychology have their conceptual roots in pragmatism and phenomenology. Secondly, an embodied vison of cognition can describe how our habits are formed from sensorimotor contingencies and are self-organizing patterns of behavior in interaction with an environment. This can be described through the metaphor of ‘laying down a path’, whereby taking a shortcut across a field of grass a path is formed, which enables walking across the field of grass. Laying down a path is more than a metaphor, but also an example of the sociomaterial dimension of habit. Habits are always formed in an interaction between an organism and an environment that is, in our case both material and social.

Formation of self-organized patterns on aluminum substrates by atmospheric pressure plasma jet for surface engineering applications

Aluminum (Al-2024) substrates were exposed to an atmospheric pressure plasma jet (APPJ) produced by a rotating arc device in air. For short nozzle-to-substrate distances, transient streamers were transferred to alter large-scale metallic surfaces. Through judicious control of the operating conditions, in particular the plasma absorbed power, air flux, distance from the jet head, scanning speed, and number of passes, self-organized patterns appeared on the aluminum substrates. Confocal surface topography, scanning electron microscopy, x-ray diffraction, and energy-dispersive x-ray spectroscopy revealed bump-like, heavily-oxidized aluminum microstructures grown on top of a layered metallic surface. Depending on the operating conditions, the bumps are either isolated or linked as serpentines. The plasma-treated surfaces with self-organized, multilayered and multiscale features identified in this work highlights a promising structure for many surface engineering applications.

Distributed information encoding and decoding using self-organized spatial patterns

SummaryDynamical systems often generate distinct outputs according to different initial conditions, and one can infer the corresponding input configuration given an output. This property captures the essence of information encoding and decoding. Here, we demonstrate the use of self-organized patterns that generate high-dimensional outputs, combined with machine learning, to achieve distributed information encoding and decoding. Our approach exploits a critical property of many natural pattern-formation systems: in repeated realizations, each initial configuration generates similar but not identical output patterns due to randomness in the patterning process. However, for sufficiently small randomness, different groups of patterns that arise from different initial configurations can be distinguished from one another. Modulating the pattern-generation and machine learning model training can tune the tradeoff between encoding capacity and security. We further show that this strategy is scalable by implementing the encoding and decoding of all characters of the standard English keyboard.

Formation of honeycomb-Kagome hexagonal superlattice pattern with dark discharges in dielectric barrier discharge

A honeycomb-Kagome hexagonal superlattice pattern with dark discharges is observed in a dielectric barrier discharge system for the first time. The spatiotemporal structure of the honeycomb-Kagome hexagonal superlattice pattern with dark discharges is investigated by an intensified charge-coupled device and the photomultipliers show that it is an interleaving of three different sub-lattices, which are bright-spot, invisible honeycomb lattice, and Kagome lattice with invisible frameworks and dim-spots, respectively. The invisible honeycomb lattices and Kagome lattices are actually composed of dark discharges. By using the optical emission spectra method, it is found that the plasma parameters of the three different sub-lattices are different. The influence of the dark discharges on pattern formation is discussed. The results may have significance for the investigation of the dark discharges and will accelerate the development of self-organized pattern dynamics.

Tunability of Self-Organized Structures Based on Thermodynamic Flux.

Nature establishes structures and functions via self-organization of constituents, including ions, molecules, and particles. Understanding the selection rule that determines the self-organized structure formed from many possible alternatives is fundamentally and technologically important. In this study, the selection rule for the self-organization associated with a reaction-diffusion system was explored using the Liesegang phenomenon, by which a periodic precipitation pattern is formed as a model system. Experiments were conducted by systematically changing the mass flux. At low mass fluxes, a vertically periodic pattern was formed, whereas at high mass fluxes, a horizontally periodic pattern was formed. The results inferred that a structural vertical-to-horizontal periodicity transition occurred in the self-organized periodic structure at the crossover flux at which the entropy production rate reversed. Numerical analyses attributed the as-observed flux-dependent structural transition to the selection of the self-organized pattern with a higher entropy production rate. These findings contribute to our understanding of how nature controls self-organized structures and geometry, potentially facilitating the development of novel designs, syntheses, and fabrication processes for well-controlled organized functional structures.

Self-organizing morphogenetic mechanisms as processors of evolution.

Many organismic shapes and ornamentations are analogous to self-organizing patterns in the non-biological world. lt is suggested that responsible processes become first serendipitously "adopted" by developmental systems and then "lamed" by Darwinian selection as soon as a specific function has been acquired. Yet, taming can only reduce, bul not eliminare, the unpredictability of the dynamic systems at the local level.

Versatile Patterns in the Actin Cortex of Motile Cells: Self-Organized Pulses Can Coexist with Macropinocytic Ring-Shaped Waves.

Self-organized patterns in the actin cytoskeleton are essential for eukaryotic cellular life. They are the building blocks of many functional structures that often operate simultaneously to facilitate, for example, nutrient uptake and movement of cells. However, identifying how qualitatively distinct actin patterns can coexist remains a challenge. Using bifurcation theory of a mass conserved activator-inhibitor system, we uncover a generic mechanism of how different actin waves-traveling waves and excitable pulses-organize and simultaneously emerge. Live-cell imaging experiments indeed reveal that narrow, planar, and fast-moving excitable pulses may coexist with ring-shaped macropinocytic actin waves in the cortex of motile amoeboid cells.

Turing-Turing bifurcation and multi-stable patterns in a Gierer-Meinhardt system

The classical Gierer-Meinhardt system portrays the formation process of a self-organizing pattern of vascular mesenchymal cells. In this paper, the coexistence of multi-stable patterns with different spatial responses and the superposition for patterns have been explored in theory from the perspective of Turing-Turing bifurcation. On the one-dimensional region, the system is simplified near the Turing-Turing singularity to obtain a third-order ordinary differential equation employing center manifold and normal form theory, which is locally topologically equivalent to the primitive system and its coefficients can be represented by the parameters of original equation. Especially, considering the simplified system, it is theoretically revealed that the system supports semi-stable patterns superimposed by two different spatial resonances and the coexistence of four stable steady states with different single characteristic wavelengths, indicating that different initial conditions may tent to completely different spatial patterns. Finally, some numerical simulations are given, which are consistent with the theoretical analysis. The multi-stable and superimposed modes of the system are also studied on a two-dimensional region, which shows that some experimental patterns of vascular mesenchymal cells in vitro can be interpreted as the superposition of different spatial modal patterns to a certain extent.

Bridging scales in a multiscale pattern-forming system

Self-organized pattern formation is vital for many biological processes. Reaction-diffusion models have advanced our understanding of how biological systems develop spatial structures, starting from homogeneity. However, biological processes inherently involve multiple spatial and temporal scales and transition from one pattern to another over time, rather than progressing from homogeneity to a pattern. To deal with such multiscale systems, coarse-graining methods are needed that allow the dynamics to be reduced to the relevant degrees of freedom at large scales, but without losing information about the patterns at small scales. Here, we present a semiphenomenological approach which exploits mass conservation in pattern formation, and enables reconstruction of information about patterns from the large-scale dynamics. The basic idea is to partition the domain into distinct regions (coarse grain) and determine instantaneous dispersion relations in each region, which ultimately inform about local pattern-forming instabilities. We illustrate our approach by studying the Min system, a paradigmatic model for protein pattern formation. By performing simulations, we first show that the Min system produces multiscale patterns in a spatially heterogeneous geometry. This prediction is confirmed experimentally by in vitro reconstitution of the Min system. Using a recently developed theoretical framework for mass-conserving reaction-diffusion systems, we show that the spatiotemporal evolution of the total protein densities on large scales reliably predicts the pattern-forming dynamics. Our approach provides an alternative and versatile theoretical framework for complex systems where analytical coarse-graining methods are not applicable, and can, in principle, be applied to a wide range of systems with an underlying conservation law.

Sharp thresholds limit the benefit of defector avoidance in cooperation on networks

Consider a cooperation game on a spatial network of habitat patches, where players can relocate between patches if they judge the local conditions to be unfavorable. In time, the relocation events may lead to a homogeneous state where all patches harbor the same relative densities of cooperators and defectors, or they may lead to self-organized patterns, where some patches become safe havens that maintain an elevated cooperator density. Here we analyze the transition between these states mathematically. We show that safe havens form once a certain threshold in connectivity is crossed. This threshold can be analytically linked to the structure of the patch network and specifically to certain network motifs. Surprisingly, a forgiving defector avoidance strategy may be most favorable for cooperators. Our results demonstrate that the analysis of cooperation games in ecological metacommunity models is mathematically tractable and has the potential to link topics such as macroecological patterns, behavioral evolution, and network topology.

Self-organized patterns at the plasma–liquid anode interface in a helium glow discharge: temporal development and mechanisms

Self-organization at the plasma–liquid anode interface is a commonly observed phenomenon for atmospheric pressure glow plasmas, resulting in patterns with distinctive shapes such as circular ring, star-shaped, and gear-like structures, depending primarily on the discharge current and solution conductivity. Recent studies have shown that the electrode gap distance, solute used for liquid anode solution, and gas composition can also significantly impact pattern formation. Nonetheless, an overarching model or explanation of the key underlying mechanisms consistent with all experimentally observed trends is not yet reported. We propose a key underlying mechanism enabling pattern formation motivated by a detailed parametric study of pattern formation complemented by the temporal development of patterns and consistent with all observed trends. Pattern formation was observed to be on a time scale of 100 μs, similar to the time scales of gas heating and evaporation. It was found that a minimum water evaporation rate of (3.5 ± 0.5) × 10−6 kg s−1 and reduced electric field in the positive column of 16.6 ± 0.4 Td is required for pattern formation in the investigated cases irrespective of solution conductivity and gas composition for NaCl solutions. Nonetheless, the presence of cations for which the corresponding metal atom has a low ionization energy was identified as a necessary condition for pattern formation. The reported results suggest that the presence of a small amount of metal atoms in the gas phase with low ionization energy enhances the overall ionization rate in the near anode region which triggers pattern formation.