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.

中文翻译：

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大自然中的艺术形式：从海克尔（Haeckel）和布拉斯卡（Blaschka）到3D纳米断层扫描，定量图像分析，演变和当代艺术的放射线虫。

19世纪末/ 20世纪末的科学家/艺术家恩斯特·海克尔（Ernst Haeckel）的插图，在他的《自然中的艺术形式》一书中进行了描述（最初德语为Kunstformen der Natur）（1898–1904），在艺术，生物学和数学的交汇处已有一个多世纪了。Haeckel的放射虫图像（在玻璃屋中被称为变形虫的微观原生动物）影响了多个世纪的艺术家（玻璃艺术家Leopold和Rudolph Blaschka；雕塑家Henry Moore；建筑师Rene Binet，Zaha Hadid，Antoni Gaudi，Chris Bosse和Frank Gehry；以及设计师-电影制作人Charles和Ray Eames）。我们将重点放在这一历史上，并通过对放射虫的3D视觉，拓扑和几何分析进行扩展，将跨学科遗产的艺术，生物学和数学贡献扩展到包括具有图论，空间统计和计算几何学的纳米尺度。我们分析了通过Haeckel的图像，光学显微镜，扫描电子显微镜，显微和纳米断层扫描以及三维计算机渲染。使用图像分析程序包“ Ka-me：A Voronoi图像分析器”进行数学分析。进一步的分析利用了三维印刷，激光蚀刻晶体玻璃艺术和雕塑。通过MorphoSource公开共享的放射虫和其他原生动物的三维纳米断层图，为艺术家，建筑师，古生物学家，结构形态学家，分类学家，博物馆馆长和数学生物学家提供了新的可能性。与众不同