Two-dimensional visualizations of dark matter structures in simulations, such as the images below, have the shortcoming that the density of dark matter has to be projected along one dimension. In order to understand the true, three-dimensional density structure, we wanted to create three-dimensional surfaces and materialize them into tangible objects using 3D printers. For this experiment, we chose the two sections of a simulation shown below: the entire simulation box and a smaller volume around a massive, growing halo.

Dark matter simulations

Visualizations of the density of dark matter in a simulation, with brighter color indicating higher density. Left: the entire volume of the simulation, about 600 million light years on a side. Right: a smaller volume around a massive, growing halo, about 230 million light years on a side.

In order to print the dark matter “shape” of these volumes, we need to simplify the density field into one closed, coherent surface. This represents a huge simplification: in the images above, we use a color scale to express the range of dark matter densities, which we now have to capture in only one surface. We chose this surface to be the contour where the density reaches a particular value, slightly higher than the mean density of the universe. The images below illustrate how we further simplify this surface to make it 3D printable.

Iso-density surfaces

Simplification of iso-density contours for 3D printing. The top row shows the entire simulation volume, the bottom row the small region around a large halo. Left: Three iso-density contours (red, orange, yellow) at 1.26, 10, and 100 times the mean density of dark matter. The orange and yellow contours are shown to highlight the densest structures, but the red contour is the one chosen for 3D printing. The surface is way too complicated for printing at this stage though. Center: The density field has been smoothed, making the contour a lot simpler. Right: Unconnected “islands” have been removed, leaving only one coherent surface.

We converted the surfaces shown on the right into 3D printable files using the Blender software. They were printed using two different machines at the Advanced Output Center at SAIC, namely a Dimension SST 1200es (for the entire simulation volume) using opaque beige plastic, and a Objet 30 Pro (for the smaller volume) using transparent plastic. The prints measure about 25 and 15 cm on a side, respectively.



In the surface of the infall region around a massive halo (second photo above), a wall of dark matter is apparent. This feature highlights one advantage of the 3D printing technique: if such a wall intersects a 2D image, it shows up as a filamentary structure instead, misleading the viewer.

The 3D surfaces shown here are publicly available as print-ready .stl files (cosmological_volume.stl, infall_region.stl). If you use them in a publication or exhibition, please credit The Fabric of the Universe for the 3D models.