An experiment in additive manufacturing
For a while I have been considering making 3D printed objects with interesting patterns and shapes, especially after seeing the work of Nervous System, which produces jewelry and other useful items modeled with algorithms (including reaction-diffusion):
My friend Britta and I were thinking about ideas for what I should make, and consequently what service I should use. We decided on Shapeways, a personalized fabrication service capable of printing 3D parts. They charge according to amount of material, so it made sense to produce something very small and light. Britta commissioned a reaction-diffusion necklace, inspired by the necklace shown above. Since I already had some working Mathematica code for generating reaction-diffusion systems, I modified the parameters slightly to create worm-like shapes that would interlock as much as possible, as the necklace would have to be made from a single connected component so it would not fall apart.
I was determined to produce this necklace in the most unusual and perverse way possible. I used Mathematica, Photoshop, and Blender to produce a 3D model of a small, flat object suitable for wearing. Here is an image of the resulting pattern:
Invariably, the result was not made of only one piece, so I broke the image into connected components using Photoshop’s paintbucket tool:
I chose the one that was both the most interesting and also of the best dimensions. I leave it as an exercise for the reader to determine which component I chose. After isolating this component in Photoshop, I saved the image as a black and white JPEG and imported it back into Mathematica, where I wrote a small program to use the darkness of each pixel to determine by how much to extrude the 3D object at that point.
My first attempts generated objects that were much too large or small, but finally after much labor, I managed to come up with something that was not rejected by Shapeways. I came up with this one, 3.3 inches wide and eligible for printing:
Very vermicular. Britta and I chose the material called “White, Strong, & Flexible” since its price, strength, robustness and appearance sounded good for a practical first-try object.
I ordered it from Shapeways (along with two more copies so that we reached the $25 minimum), but a couple weeks later I received an email saying that the model could not be printed because some elements were too thin. Frustrating! I emailed a Shapeways representative, and we figured out that some of the “neighboring” tubes had thin membranes connecting them when they got too close to one another — these were thinner than the machine’s tolerance.
I fixed my model, resubmitted it, and we waited two more weeks. And one very exciting day, I received a small box containing the objects and gave one to Britta. She bought some waxed white cord and tied a couple knots to make the necklace:
Success! Some of my friends have been complaining that it is a bit too flat compared to the possibilities of 3D printing, so I am determined to continue my 3D modeling adventure. I already ordered the Shapeways materials sample kit which will allow me to explore what kinds of materials are available for printing, as well as giving me something to play with until I decide what to make next.
