Art Forms in Nature: radiolaria from Haeckel and Blaschka to 3D nanotomography, quantitative image analysis,...

The illustrations of the late nineteenth-/twentieth-century scientist/artist Ernst Haeckel, as depicted in his book Art Forms in Nature (originally in German as Kunstformen der Natur, 1898-1904), have been at the intersection of art, biology, and mathematics for over a century. Haeckel's images of radiolaria (microscopic protozoans described as amoeba in glass houses) have influenced various artists for over a century (glass artists Leopold and Rudolph Blaschka; sculptor Henry Moore; architects Rene Binet, Zaha Hadid, Antoni Gaudi, Chris Bosse and Frank Gehry; and designers-filmmakers Charles and Ray Eames). We focus on this history and extend the artistic, biological, and mathematical contributions of this interdisciplinary legacy by going beyond the 3D visual, topological, and geometric analyses of radiolaria to include the nanoscale with graph theory, spatial statistics, and computational geometry. We analyze multiple visualizations of radiolaria generated through Haeckel's images, light microscopy, scanning electron microscopy, micro- and nanotomography, and three-dimensional computer rendering. Mathematical analyses are conducted using the image analysis package "Ka-me: A Voronoi Image Analyzer." Further analyses utilize three-dimensional printing, laser etched crystalline glass art, and sculpture. Open sharing of three-dimensional nanotomography of radiolaria and other protozoa through MorphoSource enables new possibilities for artists, architects, paleontologists, structural morphologists, taxonomists, museum curators, and mathematical biologists. Distinctively, newer models of radiolaria fit into a larger context of productive interdisciplinary collaboration that continues Haeckel's legacy that lay a foundation for new work in biomimetic design and additive manufacturing where artistic and scientific models mutually and robustly generate wonder, beauty, utility, curiosity, insight, environmentalism, theory, and questions.