Active matter comprises individually driven units that convert locally stored energy into mechanical motion. Interactions between driven units lead to a variety of nonequilibrium collective phenomena in active matter. One of such phenomena is anomalously large density fluctuations, which have been observed in both experiments and theories. Here we show that, on the contrary, density fluctuations in active matter can also be greatly suppressed. Our experiments are carried out with marine algae (Effrenium voratum), which swim in circles at the air–liquid interfaces with two different eukaryotic flagella. Cell swimming generates fluid flow that leads to effective repulsions between cells in the far field. The long-range nature of such repulsive interactions suppresses density fluctuations and generates disordered hyperuniform states under a wide range of density conditions. Emergence of hyperuniformity and associated scaling exponent are quantitatively reproduced in a numerical model whose main ingredients are effective hydrodynamic interactions and uncorrelated random cell motion. Our results demonstrate the existence of disordered hyperuniform states in active matter and suggest the possibility of using hydrodynamic flow for self-assembly in active matter.

Patterned ground, defined by the segregation of stones in soil according to size, is one of the most strikingly self-organized characteristics of polar and high-alpine landscapes. The presence of such patterns on Mars has been proposed as evidence for the past presence of surface liquid water. Despite their ubiquity, the dearth of quantitative field data on the patterns and their slow dynamics have hindered fundamental understanding of the pattern formation mechanisms. Here, we use laboratory experiments to show that stone transport is strongly dependent on local stone concentration and the height of ice needles, leading effectively to pattern formation driven by needle ice activity. Through numerical simulations, theory, and experiments, we show that the nonlinear amplification of long wavelength instabilities leads to self-similar dynamics that resemble phase separation patterns in binary alloys, characterized by scaling laws and spatial structure formation. Our results illustrate insights to be gained into patterns in landscapes by viewing the pattern formation through the lens of phase separation. Moreover, they may help interpret spatial structures that arise on diverse planetary landscapes, including ground patterns recently examined using the rover Curiosity on Mars.

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Adaptive locomotion of living organisms contributes to their competitive abilities and 1 help maintain their fitness in diverse environments. To date, understanding of 2 searching behaviours and how microscale dynamics scale up to ecosystem-level 3 processes remain poorly understood in ecology. Here, we investigate the motion 4 patterns of the biofilm-inhabiting marine diatom Navicula arenaria var. rostellata at 5 the two-dimensional space. We report that individual Navicula cells display a novel 6 "rotational run-and-reversal" movement behaviour at different concentrations of 7 dissolved silicate (dSi). Using experimental measurements of the search behaviours, 8 we show that translation motions of cells can be predicted exactly with a universal 9 model-the generalized Langevin theoretical model. Both the experimental and 10 theoretical results reveal quantitative agreement with an optimal foraging strategy 11 and show that circular and reversal behaviours both contribute to comparable spatial 12 diffusion properties. Our modelling results suggest that the evolving movement 13 behaviours of diatom cells are driven by optimization of searching their physical 14 surroundings, and predicted behavioural parameters coincide with the experimental 15observations. These optimized movement behaviours are an evolutionarily stable 16 strategy to cope with environmental complexity.

Although the diversity of spatial patterns has gained extensive attention on ecosystems, it is still a challenge to discern the underlying ecological processes and mechanisms. Dynamical system models, such partial differential equations (PDEs), are some of the most widely used frameworks to unravel the spatial pattern formation, and to explore the potential ecological processes and mechanisms. Here, comparing the similarity of patterned dynamics among Allen–Cahn (AC) model, Cahn–Hilliard (CH) model, and Cahn–Hilliard with population demographics (CHPD) model, we show that integrated spatiotemporal behaviors of the structure factors, the density-fluctuation scaling, the Lifshitz–Slyozov (LS) scaling, and the saturation status are useful indicators to infer the underlying ecological processes, even though they display the indistinguishable spatial patterns. First, there is a remarkable peak of structure factors of the CH model and CHPD model, but absent in AC model. Second, both CH and CHPD models reveal a hyperuniform behavior with scaling of −2.90 and −2.60, respectively, but AC model displays a random distribution with scaling of −1.91. Third, both AC and CH display uniform LS behaviors with slightly different scaling of 0.37 and 0.32, respectively, but CHPD model has scaling of 0.19 at short-time scales and saturation at long-time scales. In sum, we provide insights into the dynamical indicators/behaviors of spatial patterns, obtained from pure spatial data and spatiotemporal related data, and a potential application to infer ecological processes.