Every year after the full moons in late October and November, Australia’s Great Barrier Reef begins its annual spawning — first the coral species inshore, where waters are warmer, then the offshore corals, the main event. Last year, this natural spectacle coincided with the woolly propagation of two new colonies of the Crochet Coral Reef, a long-running craft-science collaborative artwork now inhabiting the Schlossmuseum in Linz, Austria, and the Carnegie Museum of Art in Pittsburgh.

To date, nearly 25,000 crocheters (“reefers”) have created a worldwide archipelago of more than 50 reefs — both a paean to and a plea for these ecosystems, rainforests of the sea, which are threatened by climate change. The project also explores mathematical themes, since many living reef organisms biologically approximate the quirky curvature of hyperbolic geometry.

Within the realm of two dimensions, geometry deals with properties of points, lines, figures, surfaces: The Euclidean plane is flat and therefore displays zero curvature. By contrast, the surface of a sphere displays constant positive curvature; at all points, the surface bends inward toward itself. And a hyperbolic plane exhibits constant negative curvature; at all points, the surface curves away from itself. Reef life thrives on hyperbolism, so to speak; the curvy surface structure of coral maximizes nutrient intake, and nudibranchs propel through water with frilly flanges.

In the artworks, marine morphologies are modeled — crocheted — with loopy verisimilitude. A bit like Monet’s water lilies, the crochet corals are abstract representations of nature, said Christine Wertheim, an artist and writer now retired from the California Institute of the Arts. Dr. Wertheim is the driving artistic force behind the project, which she created with Margaret Wertheim, her twin sister, a science writer who is in charge of scientific and mathematical components as well as management. The Wertheims, Australians who live together in Los Angeles, spun out the mother reef from their living room many moons ago, in 2005.

Crochet Coral Reef exhibitions typically have two main components: The Wertheims provide an anchor, of sorts, with works from their collection that they have crocheted over the years. They also incorporate pieces by select skilled international contributors. One is a “bleached reef,” evoking corals stressed by increases in ocean temperature; another, a “coral forest” made from yarn and plastic, laments the debris that pollutes reef systems.

Then in response to an open call, volunteers far and wide crochet a pageant of individual specimens that agglomerate in a “satellite reef,” staged by a local curatorial team with guidance from the Wertheims. The Wertheims liken this hive mind to a friendly iteration of the Borg from “Star Trek: Next Generation.” All contributors are credited.

The largest satellite reef thus far coalesced in 2022 at the Museum Frieder Burda in Baden-Baden, Germany, with some 40,000 coral pieces by about 4,000 contributors. The Wertheims call this the Sistine Chapel of crochet reefs (documented in a splashy exhibition catalog). But the show at the Linz Schlossmuseum, which is dedicated to natural science as well as art and culture, is reminiscent of the work of the painter Giuseppe Arcimboldo, whose collage portraits from depictions of fruits, vegetables and flowers are “fantastically heterogeneous, also very funny and clever,” Ms. Wertheim said…