Patterned

154 Patterned Caroline Van Hemert I’ve been thinking about mathematics lately, wondering if equations can explain the patterns I see around me. Flying over the western border of the Arctic National Wildlife Refuge in a 1974 Cessna, I stare down at the landscape from above. From this angle, tundra looks like an M. C. Escher sketch—angular shapes painted in summer’s yellow-greens. The plane banks and I press my face against scratched glass, searching for animals and birds that look like tiny pieces of dust marring a photograph. White blobs on water mean swans; on land, they typically signal the presence of a single snowy owl (at least at this time of year—any sensible polar bear would be far out of sight on the ice floes). Herds of caribou show up as brown spots en masse with occasional glimpses of antlered protrusions. A blurred coffee-colored shock of fur may be a lone musk ox or, less likely, a brown bear. The first time I flew over this landscape I couldn’t tell geese from foxes, confused shape and size and scale. We’d be flying low, and I’d mistake tussocks, ubiquitous lumps of cottongrass, for four-legged mammals. My eyes now have learned to associate patterns with creatures , to discern particular movements with shapes. But I still start in surprise when I see birds from the air, flying alongside the plane or banking beneath its metallic glimmer. I watch the undulating flight carefully, mesmerized by its motion while willing its path to arc away from mine. Birds generally don’t get snagged by the props of small planes, as they do in jets, since single-engine bush planes move slowly enough for easy dodging. But the birds seem impossibly close as I watch them pass by my window, wings pumping gracefully alongside our mechanized flight. I look down and search for designs tumbling past me in miniature. From the air, the perspective offered by distance lends well to the imagination . Like seeing elephants in a pile of cumulus clouds above—our minds always seeking familiar images, instilling order—I watch tundra 155 Caroline Van Hemert patterns morph into shapes. Fields of hexagons transform into scowling faces, turn to geometrically winged birds, and then erupt into a tiny city of buildings and cars and infrastructure. Permafrost, the constant layer of ice that lies beneath the tundra, creates this montage; ice wedges intrude into soil, gradually increasing with each cycle of freeze and thaw. In the wake of these frozen blades, honeycombed depressions arise, eventually giving way to thick-lipped ponds and beaded drainage streams. Another day, thousands of miles and hundreds of days away, I stand under the scorching midday sun in the Namib Desert. A black and white oryx, a striking desert antelope, looks down at me from above, perched on a dune like a four-legged sentinel. I crouch over the ground to examine fine fissures and deep-set gaps in the midst of what used to be a pond. These pans, sucked dry of moisture until next season’s rains, form small, ever-shrinking circles of caked mud, laid down among undulating red dunes and fine waves of sand. The sticky pond bottoms , originally saturated with standing water, begin to separate along predictable lines as evaporation leaves a hexagonal web of cracks in its wake. Bubbles aggregate into similar hexagonal patterns in seafoam, igneous rock cools into six-sided columns, rivers branch at triple junctions, all following the path of least resistance. In their honeycomb constructions , bees illustrate a model of efficiency that we have since claimed as our own. Hexagons appear in human biology as universally as they do across nature. Our center of light sensitivity, the path of visual perception itself, sees sunlight refracted through miniature honeycombs. Less than one square millimeter in size, this specialized part of our retina called the fovea functions as a lens of tiny hexagons. We see our surroundings through a mosaic of conical photoreceptors, arranged in tiny, six-sided arrays. Color spots also assemble themselves in hexagonal patterns, and we witness the mark of mathematics painted on the backs of leopards, etched across the...