Creating Radiolaria

Welcome to our first subscriber-only Patreon post, where we’re going to talk about behind the scenes, works in progress and technical details. This post is about a project we’ve started this summer to create radiolarian-like sculptures.

SEM microscopy images of radiolaria by Annick Baudrimont

If you don’t know, radiolarians are microscopic organisms that build intricate, geometric skeletons out of silica, essentially glass! They have inspired a lot of artists (including ourselves) mostly through drawings made by Ernst Haeckel. He was a 19th century naturalist who made many spectacular illustrations of microscopic life cataloged in the book: Art Forms in Nature (view on all plates on wikimedia).

Haeckel Phaeodaria (left) and Spumellaria (right)

This project got started because we were contacted by a producer at the Kunstkraftwerk Museum in Germany. I won’t reveal too much about their upcoming show, but they asked us to create a series of radiolarian-like 3D printed sculptures. While we’ve been inspired by radiolarians in the past, this was meant to be more literal. And since we already love radiolarians, we figured why not, and while we’re at it we’ll make some for ourselves too. We’re currently thinking that our first Neuron tier Patreon reward will be one-of-a-kind radiolarian 3D prints.

Making of

To design our radiolarians, we create cellular patterns on surfaces using centroidal Voronoi cells. We do this using Bruno Levy’s Geogram library. While we’ve extended this method to make highly controlled anisotropic patterns in the past, radiolarians tend to be so regular that we can really just use regular Voronoi cells out of the box. What really gives the radiolarians their radiolarian feel is their shapes and their spikes. Radiolarians come in a lot of different shapes, though they tend to be rotationally symmetric. The simplest is a sphere, so that’s what we started with. To make the spikes, we simply add a line coming out of each vertex of the cellular pattern. Now this result isn’t that organic feeling, so to give it more irregularity we randomize the spike lengths using a power law distribution. Why a power law? Well, a lot of things in nature are power laws, so it gives it an organic feeling even though it’s totally random.

A look at the software we use internally for anisotropic centroidal voronoi structures on surfaces

Then to make it into a 3D printable object, we use OpenVDB to thicken our pattern lines. We’ve added a LevelSetCapsule class to the library to allow us to make structures out of lines very similar to LevelSetSphere which is used to make shapes out of particles. The resulting mesh is then smoothed a bunch using Laplacian smoothing.

Above is a power law distribution of spikes and below is a uniform random distribution 

Our latest piece is a multilayer sphere radiolarian, which is another typology you see in nature. Here, we essentially do the same thing with a smaller sphere and a larger sphere. The smaller, interior sphere is more detailed and connects to the spiky outer sphere with random nodal connections.

Next steps

Our next steps will be adding variable macroshapes to our radiolarian generator. I also want to maybe articulate the cellular structure a little more. For the exhibit, we also plan to make other families of forms, possibly based on our Porifera project exploring minimal surface foams.