Jayson Fann is not a bird—but he does make nests. Hundreds of them, fantastically large, with flowing, radial patterns molded from the golden ratio and other mathematical codes. In the hills around California's Big Sur, Fann collects felled trees, branches, and twigs and weaves them into aeries for passersby, both winged and wing-less. Nests are universal, he says. “Every creature seeks shelter, a place of protection, and bearing children. It’s a central part of the cycle of nature.” Tall with soft features and a fondness for fedoras, Fann, 45, is a woodworker, an educator, and also a conservationist. In his one-man trade, he works almost exclusively with eucalyptus, an invasive species originally from Australia, which now swaths of California’s coastal woodlands. In the mid-19th century, the towering hardwoods were planted for use as a biofuel, says Joel McBride, a eucalyptus and environmental planning expert at UC Berkeley—as well as to serve as windbreaks and a...