Mechanism Of Pattern Formation Research Articles

Helfrich-Hurault elastic instabilities driven by geometrical frustration

The Helfrich-Hurault instability is a well-known mechanism behind the undulations that occur as a result of strain upon liquid crystal systems with periodic ground states. In this review, the Helfrich-Hurault elastic instability is examined with a focus on layered liquid crystals that are geometrically frustrated. The frustration is relieved by undulations in the layered structure to maintain the preferred layer spacing. Examples of cholesteric and smectic liquid crystals confined between two spherical fluid interfaces are described and the effects of topological constraints, anchoring conditions, and curvature on the instability are examined. Lastly, the Helfrich-Hurault instability is surveyed as a pattern formation mechanism across a range of materials, both biological and synthetic.

Diffusion-assisted growth of periodic patterns on metal surfaces

Periodic patterns formed on various solid surfaces could seriously affect the properties of materials. Understanding the underlying mechanism is a key step to apply and control pattern formation in many fields. In this work, periodic patterns induced by low-energy plasma exposures on tungsten surfaces are observed and related new formation mechanisms are developed. Results from experiments and computer simulations demonstrate that atom diffusion accelerated by low energy and high flux exposures is the dominant mechanism for pattern formation. Furthermore, a similar pattern formation has been confirmed by plasma exposure experiments on molybdenum. Based on this mechanism, patterns with controllable shape have been successfully prepared on tungsten surface by adjusting plasma exposure parameters, which may provide a new understanding of pattern formation and related surface damage in tungsten induced by plasma exposures.

Mineralogy and geochemistry of pattern formation in zebra rock from the East Kimberley, Australia

Rhythmic patterns are widespread in geological materials. A particularly striking, macroscale example is zebra rock from the East Kimberley region of northwestern Australia. The rock is famous for its distinctive, rhythmically ordered, iron-oxide pattern, which transforms an Ediacaran-aged siltstone into an attractive semi-precious gemstone. Several different formation mechanisms of this pattern have been proposed in previous studies, with the two most prominent being redoximorphic banding in acid-sulfate soils and Liesegang banding in an acidic hydrothermal system. Using a combination of mineralogy, geochemistry and geological context, this study attempts to confirm both the occurrence and relative timing of acid-sulfate fluid rock interactions in zebra rock and seeks to determine whether pedogenic processes or hydrothermal alteration can better explain the origin of these patterns. We present the first evidence that the iron-oxide banding developed simultaneously with a period of aluminosilicate dissolution, clay precipitation, and fluid flow, consistent with the infiltration of an acidic fluid. This conclusion was evidenced through the hexagonal-platelet morphology of the hematite pigment, kaolinite-hematite textural relationships, and a paleoflow direction preserved in the asymmetric intensity of the hematite concentration. However, while the mineralogy of zebra rock strongly suggests interactions with acid-sulfates, the origin and temperature of the fluid could not be conclusively determined. Supporting a hydrothermal origin, a thorough analysis of zebra rock mineralogy revealed a mineral assemblage consistent with advanced argillic hydrothermal alteration, wherein pyrophyillite, kaolinite, and dickite indicate minimum palaeotemperatures upwards of 120 °C and the presence of alunite and a svanbergite-woodhouseite solid solution suggests oxidising, acidic (pH <5) conditions. The low Rb/Sr ratio and relative immobility of rare earth elements in most zebra rock deposits are also consistent with an acidic hydrothermal origin. Further support was also observed in the mineralogical trends between examined outcrops, grading from alunite-type to kaolinite/dickite-type facies in a south-west direction. But despite this evidence, the acid-sulfate soil hypothesis could not be refuted and was itself supported by the large number of pyrite dissolution voids both underlying and within the patterned layer. Furthermore, the consistent compaction of reduction spheroids, dissolution voids, and pseudomorphic inclusions within the light banding of zebra rock are in agreement with near-surface supergene weathering, ruling out hypogene hydrothermal alteration. A mechanism of pattern formation is proposed whereby zebra rock banding is formed by the Liesegang phenomenon, driven by the oxidation of Fe2+ ions during the infiltration of an Fe2+-rich, acid-sulfate fluid into oxidising host sediments.

Pulsed Interaction Signals as a Route to Biological Pattern Formation

We identify a mechanism for biological spatial pattern formation arising when the signals that mediate interactions between individuals in a population have pulsed character. Our general population-signal framework shows that while for a slow signal-dynamics limit no pattern formation is observed for any values of the model parameters, for a fast limit, on the contrary, pattern formation can occur. Furthermore, at these limits, our framework reduces, respectively, to reaction-diffusion and spatially nonlocal models, thus bridging these approaches.

Spatial Evolution and Multi-Scenario Simulation of Rural “Production–Ecological–Living” Space: A Case Study for Beijing, China

With the vigorous development of industrialization and urbanization, rural space faces many difficulties in achieving sustainable development, such as the spatial structure being unbalanced. To explore the sustainable development of rural space, this study evaluates the spatial evolution and multi-scenario simulation of rural space with reference to the three dominant functions of land use, namely “production–ecological–living” (PEL), based on the interpretation of land use remote sensing data in 2000, 2010, and 2020. The change characteristics and the formation mechanism of the territorial spatial pattern were quantitatively analyzed by gravity center transfer, territorial spatial transfer matrix, standard deviational ellipse, geo-detector, and artificial neural network CA simulation. The results showed that (1) from 2000 to 2020, the rural production space in Beijing continued to decrease, the rural living space continued to increase and then gradually contracted, and the rural ecological space as a whole also showed a downward trend. (2) During the study period, the formation and evolution of the ecological spatial pattern of rural production and living in Beijing were affected by both regional physical geographical factors and human, social, and economic factors, with significant differences; the interaction between two driving factors is stronger than that within a single factor, and the main mode of action is double factor enhancement and nonlinear enhancement. (3) Compared with the other three scenarios, the performance of Beijing’s rural space in 2030 under the harmonious development scenario is more compact and stable, the rural production space is basically guaranteed, the intensity of rural living space is enhanced, and the overall situation of rural ecological space is stable. Our results show that in the future decision-making of rural land and space development around a metropolis, we should fully consider the evolution law of rural spatial pattern, as well as the driving force of natural geographical factors and economic activity factors and discuss the optimization and overall management of rural production and living ecological space through multi-scenario spatial simulation.

Experimental study on the ultimate bearing capacity of damaged RC arches strengthened with ultra-high performance concrete

With the deterioration of the infrastructure and the increasing traffic volume, the service performance of bridge structures dramatically dropped. Strengthening and retrofitting these bridges with ultra-high-performance concrete (UHPC) can effectively improve their mechanical properties and durability. In this paper, the experimental investigation of the behavior of damaged RC arches strengthened with UHPC is presented. Three strengthened arches, including one arch strengthened with C50 (RC1-C50) and two arches strengthened with UHPC (RC2-UHPC, RC3-UHPC), were tested under asymmetric load. Load-deflection behavior, crack propagation pattern and hinge formation mechanism are extensively studied. Results indicated that the initial crack load and ultimate bearing capacity of composite arches strengthened by UHPC were respectively enhanced by 185% and 186%, showing good effects of strengthening and toughening on the original arch. On the premise of closing the cracks in the original arch ring, the stiffness and ductility of the composite arch strengthened with UHPC (RC2-UHPC) were improved by 58% and 34%, respectively. Different from the arch strengthened with C50 (RC1-C50), no obvious cracking and separation phenomena were observed in the interface of composite arches strengthened with UHPC in the whole process of eccentric loading. The combination of keyway and planting bar (rigid and flexible) can provide reliable bonding between the UHPC and the original structure. Finally, the calculation model for predicting the cracking load and ultimate capacity of the composite arches were proposed, and the calculation results are in good agreement with the experimental results.

Mechanisms underlying the formation of complex color patterns on Nigella orientalis (Ranunculaceae) petals.

Complex color patterns on petals are widespread in flowering plants, yet the mechanisms underlying their formation remain largely unclear. Here, by conducting detailed morphological, anatomical, biochemical, optical, transcriptomic, and functional studies, we investigated the cellular bases, chromogenic substances, reflectance spectra, developmental processes, and underlying mechanisms of complex color pattern formation on Nigella orientalis petals. We found that the complexity of the N. orientalis petals in color pattern is reflected at multiple levels, with the amount and arrangement of different pigmented cells being the key. We also found that biosynthesis of the chromogenic substances of different colors is sequential, so that one color/pattern is superimposed on another. Expression and functional studies further revealed that a pair of R2R3-MYB genes function cooperatively to specify the formation of the eyebrow-like horizontal stripe and the Mohawk haircut-like splatters. Specifically, while NiorMYB113-1 functions to draw a large splatter region, NiorMYB113-2 functions to suppress the production of anthocyanins from the region where a gap will form, thereby forming the highly specialized pattern. Our results provide a detailed portrait for the spatiotemporal dynamics of the coloration of N. orientalis petals and help better understand the mechanisms underlying complex color pattern formation in plants.

Appearance and suppression of Turing patterns under a periodically forced feed

Turing instability is a general and straightforward mechanism of pattern formation in reaction–diffusion systems, and its relevance has been demonstrated in different biological phenomena. Still, there are many open questions, especially on the robustness of the Turing mechanism. Robust patterns must survive some variation in the environmental conditions. Experiments on pattern formation using chemical systems have shown many reaction–diffusion patterns and serve as relatively simple test tools to study general aspects of these phenomena. Here, we present a study of sinusoidal variation of the input feed concentrations on chemical Turing patterns. Our experimental, numerical and theoretical analysis demonstrates that patterns may appear even at significant amplitude variation of the input feed concentrations. Furthermore, using time-dependent feeding opens a way to control pattern formation. The patterns settled at constant feed may disappear, or new patterns may appear from a homogeneous steady state due to the periodic forcing.

Time-Lapse Imaging and Morphometric Analysis of Tracheal Development in Drosophila.

Detailed and quantitative analyses of the cellular events underlying the formation of specific organs or tissues is essential to understand the general mechanisms of morphogenesis and pattern formation. Observation of live tissues or whole-mount fixed specimens has emerged as the method of choice for identifying and quantifying specific cellular and tissular structures within the organism. In both cases, cell and subcellular structure identification and good quality image acquisition for these analyses are essential. Many markers for live imaging and fixed tissue are now available for detecting cell membranes, subcellular structures, and extracellular structures like the extracellular matrix (ECM). Combination of live imaging and analysis of fixed tissue is ideal to obtain a general and detailed picture of the events underlying embryonic development. By applying morphometric methods to both approaches, we can, in addition, obtain a quantitative evaluation of the specific parameters under investigation in morphogenetic and cell biological studies. In this chapter, we focus on the development of the tracheal system of Drosophila melanogaster, which provides an ideal paradigm to understand the formation of branched tubular organs. We describe the most used methods of imaging and morphometric analysis in tubulogenesis using mainly (but not exclusively) examples from embryonic development. We cover embryo preparation for fixed and live analysis of tubulogenesis, together with methods to visualize larval tracheal terminal cell branching and lumen formation. Finally, we describe morphometric analysis and quantification methods using fluorescent images of tracheal cells.

Evidence for scale-dependent root-antation feedback and its role in halting the spread of a pantropical shrub into an endemic sedge.

Vegetation pattern formation is a widespread phenomenon in resource-limited environments, but the driving mechanisms are largely unconfirmed empirically. Combining results of field studies and mathematical modeling, empirical evidence for a generic pattern-formation mechanism is demonstrated with the clonal shrub Guilandina bonduc L. (hereafter Guilandina) on the Brazilian island of Trindade. The mechanism is associated with water conduction by laterally spread roots and root augmentation as the shoot grows-a crucial element in the positive feedback loop that drives spatial patterning. Assuming precipitation-dependent root-shoot relations, the model accounts for the major vegetation landscapes on Trindade Island, substantiating lateral root augmentation as the driving mechanism of Guilandina patterning. Guilandina expands into surrounding communities dominated by the Trindade endemic, Cyperus atlanticus Hemsl. (hereafter Cyperus). It appears to do so by decreasing the water potential in soils below Cyperus through its dense lateral roots, leaving behind a patchy Guilandina-only landscape. We use this system to highlight a novel form of invasion, likely to apply to many other systems where the invasive species is pattern-forming. Depending on the level of water stress, the invasion can take two distinct forms: (i) a complete invasion at low stress that culminates in a patchy Guilandina-only landscape through a spot-replication process, and (ii) an incomplete invasion at high stress that begins but does not spread, forming isolated Guilandina spots of fixed size, surrounded by bare-soil halos, in an otherwise uniform Cyperus grassland. Thus, drier climates may act selectively on pattern-forming invasive species, imposing incomplete invasion and reducing the negative effects on native species.

Turing pattern selection for a plant–wrack model with cross-diffusion

We investigate the Turing instability and pattern formation mechanism of a plant–wrack model with both self-diffusion and cross-diffusion terms. We first study the effect of self-diffusion on the stability of equilibrium. We then derive the conditions for the occurrence of the Turing patterns induced by cross-diffusion based on self-diffusion stability. Next, we analyze the pattern selection by using the amplitude equation and obtain the exact parameter ranges of different types of patterns, including stripe patterns, hexagonal patterns and mixed states. Finally, numerical simulations confirm the theoretical results.

Turing patterns in systems with high-order interactions

Turing theory of pattern formation is among the most popular theoretical means to account for the variety of spatio-temporal structures observed in Nature and, for this reason, finds applications in many different fields. While Turing patterns have been thoroughly investigated on continuous support and on networks, only a few attempts have been made towards their characterization in systems with higher-order interactions. In this paper, we propose a way to include group interactions in reaction–diffusion systems, and we study their effects on the formation of Turing patterns. To achieve this goal, we rewrite the problem originally studied by Turing in a general form that accounts for a microscopic description of interactions of any order in the form of a hypergraph, and we prove that the interplay between the different orders of interaction may either enhance or repress the emergence of Turing patterns. Our results shed light on the mechanisms of pattern-formation in systems with many-body interactions and pave the way for further extensions of Turing original framework.

Pattern formation and front stability for a moving-boundary model of biological invasion and recession

We investigate pattern formation in a two-dimensional (2D) Fisher–Stefan model, which involves solving the Fisher–KPP equation on a compactly-supported region with a moving boundary. The boundary evolves analogously to the classical one-phase Stefan problem, such that boundary speed is proportional to the local population density gradient. By combining the Fisher–KPP and classical Stefan theory, the Fisher–Stefan model alleviates two limitations of the Fisher–KPP equation for biological populations. Unlike the Fisher–KPP equation, solutions to the Fisher–Stefan model have compact support, explicitly defining the region occupied by the population. Furthermore, the Fisher–Stefan model admits travelling wave solutions with non-negative density for all wave speeds c∈(−∞,∞), and can thus model both population invasion and population recession. In this work, we investigate whether the 2D Fisher–Stefan model predicts pattern formation, by analysing the linear stability of planar travelling wave solutions to sinusoidal transverse perturbations. Planar fronts of the Fisher–KPP equation are linearly stable. Similarly, we demonstrate that invading planar fronts (c>0) of the Fisher–Stefan model are linearly stable to perturbations of all wave numbers. However, our analysis demonstrates that receding planar fronts (c<0) of the Fisher–Stefan model are linearly unstable for all wave numbers. This is analogous to unstable solutions for planar solidification in the classical Stefan problem. Introducing a surface tension regularisation stabilises receding fronts for short-wavelength perturbations, giving rise to a range of unstable modes and a most unstable wave number. We supplement linear stability analysis with level-set numerical solutions that corroborate theoretical results. Overall, front instability in the Fisher–Stefan model suggests a new mechanism for pattern formation in receding biological populations.

Integrating theory and experiments to link local mechanisms and ecosystem-level consequences of vegetation patterns in drylands

Self-organized spatial patterns of vegetation are frequent in drylands and, because pattern shape correlates with water availability, they have been suggested as important indicators of ecosystem health. However, the mechanisms underlying pattern emergence remain unclear. Some theories hypothesize that patterns could result from a water-mediated scale-dependent feedback (SDF) whereby interactions favoring plant growth dominate at short distances and growth–inhibitory interactions dominate in the long range. However, we know little about how the presence of a focal plant affects the fitness of its neighbors as a function of the inter-individual distance, which is expected to be highly ecosystem-dependent. This lack of empirical knowledge and system dependency challenge the relevance of SDF as a unifying theory for vegetation pattern formation. Assuming that plant interactions are always inhibitory and only their intensity is scale-dependent, alternative theories also recover the typical vegetation patterns observed in nature. Importantly, although these alternative hypotheses lead to visually indistinguishable patterns, they predict contrasting desertification dynamics, which questions the potential use of vegetation patterns as ecosystem-state indicators. To help resolve this issue, we first review existing theories for vegetation self-organization and their conflicting predictions about desertification dynamics. Second, we discuss potential empirical tests via manipulative experiments to identify pattern-forming mechanisms and link them to specific desertification dynamics. A comprehensive view of models, the mechanisms they intend to capture, and experiments to test them in the field will help to better understand both how patterns emerge and improve predictions on the fate of the ecosystems where they form.

Rate-Dependent Pattern Evolution in Peeling Adhesive Tape Driven by Cohesive Failure.

In the case of low-rate peeling, an adhesive can undergo a large tensile deformation through the viscous flow and form the fingering pattern at the peeling interface, resulting in homogeneous stripes on the peeled surface. In the case of high-rate peeling, no larger viscous deformation occurs, and no surface patterns will be generated. However, it is still unclear how the surface pattern evolves when an adhesive is peeled from a relatively low rate to a high rate. Here, by peeling an adhesive tape at 180° over a wide range of rates, we find that the adhesive tape can undergo a steady peeling. As the peeling rate increases, it is observed that the surface pattern in the peeled adhesive tape tends to evolve from the initial striped pattern to a crescent pattern, then to a spotted pattern. Even in the case of the stick-slip peeling at a small angle, the patterned region also presents the same evolutionary trend. By exploiting a high-speed camera to track the deformation process of the adhesive, it is found that this evolution is actually driven by the cohesive failure of the peeling adhesive. We describe the failure process, revealing the formation mechanism of the crescent pattern. We also discuss the effect of the peeling rate on the interface instability morphology by combining the finite element simulations, elucidating how the surface pattern evolves with the peeling rate.

Determining the role of advection in patterning by bone morphogenetic proteins through neural network model-based acceleration of a 3D finite element model of the zebrafish embryo

Embryonic development is a complex phenomenon that integrates genetic regulation and biomechanical cellular behaviors. However, the relative influence of these factors on spatiotemporal morphogen distributions is not well understood. Bone Morphogenetic Proteins (BMPs) are the primary morphogens guiding the dorsal-ventral (DV) patterning of the early zebrafish embryo, and BMP signaling is regulated by a network of extracellular and intracellular factors that impact the range and signaling of BMP ligands. Recent advances in understanding the mechanism of pattern formation support a source-sink mechanism, however, it is not clear how the source-sink mechanism shapes the morphogen patterns in three-dimensional (3D) space, nor how sensitive the pattern is to biophysical rates and boundary conditions along both the anteroposterior (AP) and DV axes of the embryo, nor how the patterns are controlled over time. Throughout blastulation and gastrulation, major cell movement, known as epiboly, happens along with the BMP-mediated DV patterning. The layer of epithelial cells begins to thin as they spread toward the vegetal pole of the embryo until it has completely engulfed the yolk cell. This dynamic domain may influence the distributions of BMP network members through advection. We developed a Finite Element Model (FEM) that incorporates all stages of zebrafish embryonic development data and solves the advection-diffusion-reaction Partial Differential Equations (PDE) in a growing domain. We use the model to investigate mechanisms in underlying BMP-driven DV patterning during epiboly. Solving the PDE is computationally expensive for parameter exploration. To overcome this obstacle, we developed a Neural Network (NN) metamodel of the 3D embryo that is accurate and fast and provided a nonlinear map between high-dimensional input and output that replaces the direct numerical simulation of the PDEs. From the modeling and acceleration by the NN metamodels, we identified the impact of advection on patterning and the influence of the dynamic expression level of regulators on the BMP signaling network.

Data-driven emergence of convolutional structure in neural networks

Exploiting data invariances is crucial for efficient learning in both artificial and biological neural circuits. Understanding how neural networks can discover appropriate representations capable of harnessing the underlying symmetries of their inputs is thus crucial in machine learning and neuroscience. Convolutional neural networks, for example, were designed to exploit translation symmetry, and their capabilities triggered the first wave of deep learning successes. However, learning convolutions directly from translation-invariant data with a fully connected network has so far proven elusive. Here we show how initially fully connected neural networks solving a discrimination task can learn a convolutional structure directly from their inputs, resulting in localized, space-tiling receptive fields. These receptive fields match the filters of a convolutional network trained on the same task. By carefully designing data models for the visual scene, we show that the emergence of this pattern is triggered by the non-Gaussian, higher-order local structure of the inputs, which has long been recognized as the hallmark of natural images. We provide an analytical and numerical characterization of the pattern formation mechanism responsible for this phenomenon in a simple model and find an unexpected link between receptive field formation and tensor decomposition of higher-order input correlations. These results provide a perspective on the development of low-level feature detectors in various sensory modalities and pave the way for studying the impact of higher-order statistics on learning in neural networks.

Durability of Aligned Microtubules Dependent on Persistence Length Determines Phase Transition and Pattern Formation in Collective Motion.

Collective motion is a ubiquitous phenomenon in nature. The collective motion of cytoskeleton filaments results mainly from dynamic collisions and alignments; however, the detailed mechanism of pattern formation still needs to be clarified. In particular, the influence of persistence length, which is a measure of filament flexibility, on collective motion is still unclear and lacks experimental verifications although it is likely to directly affect the orientational flexibility of filaments. Here, we investigated the collective motion of microtubules with different persistence lengths using a microtubule-kinesin motility system. We showed that local interactions between microtubules significantly vary depending on their persistence length. We demonstrated that the bundling of microtubules is enhanced by more durable alignment, rather than by greater likelihood of alignment. An agent-based computational model confirmed that the rigidity-dependent durability of microtubule alignment dominates their collective behavior.

Size distribution of the quasi-circular vegetation patches in the Yellow River Delta, China

Recent empirical studies have suggested that the patch-size distribution of vegetation can be fitted by a power law, truncated power law, or lognormal model to provide explanatory mechanisms for vegetation pattern formation in arid and semiarid regions. However, contradictory results have been reported. Therefore, additional empirical studies are necessary to test the patch-size distribution of vegetation over several regions before it can be considered as an indicator for assessing the discontinuous transition of ecosystems and understanding the mechanisms of vegetation pattern formation. Analogous to arid and semiarid regions of the world, vegetation patterns are characterized by a two-phase mosaic composed of dense vegetation patches interspersed with areas of bare soil, referred to as quasi-circular vegetation patches (QVPs), in the Yellow River Delta (YRD), China. However, research on the patch-size distribution of the QVPs reflecting vegetation patterns and ecosystem functioning is lacking. To fill this gap, for the first time, we examined the patch-size distribution of the QVPs using the fused IKONOS high-spatial-resolution image and evaluated the statistical distributions that better fit the patch size data of the QVPs in the YRD. We found that a power law, truncated power law, or lognormal distribution was not supported in the study area, whereas gamma distribution reasonably fits the size data of QVPs, implying that micro-depressions, combined with the water-limited and salinization environments had considerable effects on vegetation pattern formation. Our results provide helpful insights and suggest that further studies are needed to classify different types of QVPs. Additionally, more efficient approaches need to be used to fit the statistical distributions for elucidating the spatial vegetation patterns in the YRD.

Evolution Characteristics and Driving Mechanism of the Territorial Space Pattern in the Yangtze River Economic Belt, China

Scientific understanding of the evolution law of territorial space patterns and the ability to reveal the formation mechanism hold great significance for the sustainable utilization of territorial resources and the high-quality green development of the Yangtze River Economic Belt (YREB). In this study, we used the spatial chord diagram, landscape pattern index, and geographical probe to explore the evolution characteristics and formation mechanism of the territorial space pattern of the YREB from 2000 to 2020. The results showed the following: (1) The territorial space showed obvious geographical hierarchical distribution characteristics in the topographic gradient. Production and living space was dominant throughout the low and middle terrain region. Ecological space was dominant throughout the high-terrain regions. With the increase of altitude and slope, production and living space contracted, whereas ecological space areas expanded. (2) Since 2000, the territorial space has changed more dramatically. Over time, living space tended to increase, and production and ecological space tended to decrease, but ecological space was always dominant. In space, the geographical differentiation of territorial space was more obvious, and the pattern was relatively stable, with production space distributed primarily in the middle and lower reaches, living space distributed primarily in the lower reaches, and ecological space distributed primarily in the middle and upper reaches. The inter-transformation between territorial spaces was more frequent, and the transformation trajectory was diversified. (3) The fragmentation, heterogeneity, and dispersion of territorial space landscape patches throughout the whole region increased, and the balance and diversity of territorial space utilization improved. (4) Natural factors have continued to weaken the intensity of their effect on territorial space. Human factors gradually increased the extent of their interference in the territorial space. There are significant differences in the extent of the role of these different factors on the territorial space of the whole region and each basin. Natural and human factors jointly promoted the formation and development of the territorial space pattern.