Shell 4

A small shell model shows the power of mathematics to reflect the laws of nature.The organism always needs a similarly shaped home as it grows, which is modeled by a generating curve (in this case a distorted ellipse) following an exponential spiral that expands at a similar rate to that at which it drops and moves out from the central axis. This shell was created in Mathematica using the formulas developed by Deborah Fowler et al (Siggraph '92). It was solidified.in Meshlab, and touched up with Netfabb Cloud. The mesh was created by a routine which perforates the polygons to a minimum width; their edges were thickened by the Meshlab "marching cubes" algorithm. It is printable in white or colored plastic, and metals which accept a .9mm minimum wire dimension. Contact me if interested either in the mathematics or in a model printable in other materials.