Francesco de Comité is an Associate Professor in Computer Science at the University of Sciences in Lille, France, where he researches the 2D and 3D representation of mathematical concepts and objects. He’s presented papers on a variety of topics including anamorphoses, experiments in circle packing, and Dupin cyclides. His current project involves modeling and 3D printing sea shells. He’ll be presenting a paper on the topic at Bridges Conference in July. You can find his projects on Flickr as well as on Shapeways.

Hackaday: One of your recent projects involves creating fractal patterns and warping them into biologically-correct sea shell shapes, which you then print.

FdC: Modeling seashell shapes is an old topic–Moseley, 1838, D’Arcy Thompson beginning of 20th century. A seashell can be defined as a curve turning around an axis, while translating in the direction of this axis (i.e. on a helicoidal trajectory), and growing in size at the same time. This was modeled for computers in the ’60s by David Raup.

Drawing patterns on seashells was described by Hans Meinhardt using a model of chemical reactions (activator-inhibitor), in the same spirit as Turing’s work on morphogenesis. Combining these two works, and using 3D printers instead of 2D renderers, we can build realistic seashells, either by copying existing shells, or inventing new ones. A 3D model is not just a juxtaposition of a huge number of 2D views: manipulating 3D models can help you understand the object, find details, and so on.

I was curious to see if making a 3D seashell was possible. Moreover, I show that this can be done with simple tools — well, except the 3D printer.
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