We investigate a new form of collective dynamics displayed by Thiovulum majus, one of the fastest-swimming bacteria known. Cells spontaneously organize on a surface into a visually striking two-dimensional hexagonal lattice of rotating cells. As each constituent cell rotates its flagella, it creates a tornadolike flow that pulls neighboring cells towards and around it. As cells rotate against their neighbors, they exert forces on one another, causing the crystal to rotate and cells to reorganize. We show how these dynamics arise from hydrodynamic and steric interactions between cells. We derive the equations of motion for a crystal, show that this model explains several aspects of the observed dynamics, and discuss the stability of these active crystals.

Stromatolites document microbial interactions with sediments and flowing water throughout recorded Earth history and have the potential to illuminate the long-term history of life and environments. Modern stromatolites, however, provide analogs to only a small subset of the structures preserved in Archean and Proterozoic carbonates. Thus, interpretations of secular trends in the shapes and textures of ancient columnar stromatolites require nonuniformitarian, scale-dependent models of microbial responses to nutrient availability, seawater chemistry, influx of sediment grains, shear, and burial. Models that integrate stromatolite scales, macroscopic organization, and shapes could also help test the biogenicity of the oldest stromatolites and other structures whose petrographic fabrics do not preserve direct evidence of microbial activity. An improved understanding of stromatolite morphogenesis in the presence of oxygenic and anoxygenic microbial mats may illuminate the diversity of microbial metabolisms that contributed to stromatolite growth in early oceans.

The geometric complexity of stream networks has been a source of fascination for centuries. However, a comprehensive understanding of ramification-the mechanism of branching by which such networks grow-remains elusive. Here we show that streams incised by groundwater seepage branch at a characteristic angle of 2π/5 = 72°. Our theory represents streams as a collection of paths growing and bifurcating in a diffusing field. Our observations of nearly 5,000 bifurcated streams growing in a 100 km 2 groundwater field on the Florida Panhandle yield a mean bifurcation angle of 71.9°± 0.8°. This good accord between theory and observation suggests that the network geometry is determined by the external flow field but not, as classical theories imply, by the flow within the streams themselves.river networks | network growth | Laplacian growth

Conical stromatolites are thought to be robust indicators of the presence of photosynthetic and phototactic microbes in aquatic environments as early as 3.5 billion years ago. However, phototaxis alone cannot explain the ubiquity of disrupted, curled, and contorted laminae in the crests of many Mesoproterozoic, Paleoproterozoic, and some Archean conical stromatolites. Here, we demonstrate that cyanobacterial production of oxygen in the tips of modern conical aggregates creates contorted laminae and submillimeter-to-millimeter-scale enmeshed bubbles. Similarly sized fossil bubbles and contorted laminae may be present only in the crestal zones of some conical stromatolites 2.7 billion years old or younger. This implies not only that cyanobacteria built Proterozoic conical stromatolites but also that fossil bubbles may constrain the timing of the evolution of oxygenic photosynthesis.

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