“Dark” in “dark matter” suggests something sinister, as in the “dark side of the force” (also space-related). But, as we like to think everything in physics is, dark matter is morally neutral. If anything, it is beneficial, forming the gravitational seeds for galaxies like ours, and holding galaxies together. (Dark energy, less comfortingly, drives distant galaxies faster and faster apart.)

Halloween 2017 has also been declared Dark Matter Day, suggesting unfairly that dark matter is scary. Arguably, it is a bit otherworldly, relating to Halloween. In the standard picture, the world of dark matter interacts only through gravity with our normal-matter world. Each galaxy in the normal-matter world has a corresponding puffier, bigger twin in its same location, a “dark-matter halo.”

Some very recent work of ours uncovered an even better reason than otherworldliness to celebrate this joint “All Dark-Matter-Haloes’ Eve”: spiderwebs! The arrangement of dark matter in the universe is called the cosmic web, and looks like this, with dark matter in ghostly white:

COURTESY RALF KÄHLER (KIPAC/SLAC/STANFORD), SIMULATION BY OLIVER HAHN & TOM ABEL The dark matter, a cosmic, ghostly-white web, in a cosmological computer simulation.

For the Hayden Planetarium’s “Dark Universe” planetarium show, scientific visualization expert Ralf Kähler rendered it with a color scheme that I like even better, like light shining through a folded-up structure, and with yellow beacons where galaxies might form:

Courtesy Ralf Kähler (KIPAC/SLAC/Stanford), simulation by Oliver Hahn & Tom Abel A computer-simulated cosmic web, as though backlit, shining through layers of folded-up origami. The densest places are where galaxies might be, colored yellow. See animation of how this structure evolves.

We showed that the cosmic web, with a couple of small simplifying assumptions, has the geometric properties of a “spiderweb,” a term in structural engineering. (Assumptions: we neglect structure within galaxies, and filaments and clusters of galaxies; also, some random thin threads may be necessary to sample empty voids.) Spiderwebs are, of course, Halloweeny; throughout the Halloween-celebrating world, they get stretched across porches, sometimes even across trick-or-treaters.

Many have noticed the spiderweb quality of the cosmic web. Perhaps most prominently, Tomás Saraceno has made room-sized installations of webs by black widow spiders, blown up in scale enormously, that suggest the cosmic web. An example is 14 Billions (working title):

14 billions (working title), 2010 Installation view at Bonniers Konsthall, Stockholm. Courtesy the artist; Tanya Bonakdar Gallery, New York; Andersen's Contemporary, Copenhagen; Pinksummer contemporary art, Genoa; Esther Schipper, Berlin. © Photography by Studio Tomás Saraceno, 2010

“14 Billions” refers to the the age of the universe in years, and to cosmic structure. But Saraceno included “(working title)” in the title because of the uncertain relationship between arachnid and cosmic webs. Indeed, in HuffPost, Mario Livio mentioned “the visual (although clearly not physical) similarity between spider webs and the cosmic web.” But as we found, there is a physical similarity!

What we showed is that the cosmic web is exactly (in a particular good approximation) a structural-engineering spiderweb: a network of structural members between nodes that can be strung up to be entirely in tension. An obvious example of a structural-engineering spiderweb: webs built by a spiders, which are typically entirely in tension. These networks can also be constructed entirely in compression, like a building, or tree. “Spiderweb” was coined in this context around 1980, in the structural topology group at the University of Montreal (see this chapter of the fascinating book Shaping Space). It is a concept in graphic statics, a field that James Clerk Maxwell (most famous for uniting electricity and magnetism) largely founded.

An aside about architecture: graphic statics enabled some beautiful structures of the late 19th century, such as the Eiffel Tower. In fact, the chief designer of the Eiffel Tower, Maurice Koechlin (no, not Gustave Eiffel!) wrote only one non-engineering article, “The Spider and His Web” (1905). In the 20th century, computations took over from purely geometric methods on drafting tables, and graphic statics declined, but it is now resurging in interest. A prominent advocate is Bill Baker, the structural engineer of the Burj Khalifa, the current tallest building in the world.

What does this have to do with dark matter? Imagine there were (imaginary) tiny threads connecting a lattice of nearly evenly spaced dark-matter particles, right after the Big Bang. The universe has always been expanding, but if we zoom out at the same time as it is expanding, a time sequence of these threads in a 2D universe would look something like this:

Fig. 6 of https://arxiv.org/abs/1710.04509 A time sequence of an example cosmic spiderweb.

Some squares expand faster than average, gravity like a haunted-house explorer clearing a gap through strands of a spiderweb. And some contract, and even disappear, crushed between others. Where they are crushed, strands pile up, as in the blood-red strands below, known as filaments. The gas accompanying the dark matter in filaments has very recently been detected.

From https://github.com/jhidding/adhesion-example/blob/master/notebook/Adhesion.ipynb by my coauthor, Johan Hidding.

In structural engineering, thicker filaments, piled up from many smaller ones, would carry heavier loads if it were strung up in tension. This looks a lot like a circulatory system, or a system of roads. And there is a reason for the similar structure: the red filaments act as conduits carrying matter away from a volume of space in an efficient manner; blood vessels act in the opposite direction, carrying nutrients to a volume of living tissue in the most efficient manner.

Here is a nice instructive video by my co-authors about how the structure forms with time:

One last connection, to origami: the same spiderweb structure occurring in architecture and the cosmos also is the type of pattern that can be constructed as an origami tessellation, as shown by origamist and former physicist Robert J. Lang. Here are my origami and “spiderweb” renditions of the Milky Way (the most central node) and the nearest dozen or so large galaxies around it, that happen to be in a very flattened plane:

© 2017 Mark Neyrinck, also appearing in https://arxiv.org/abs/1710.04509 Origami and textile versions of the structure in the local sheet of galaxies, aka the Council of Giants. The middle node is the Milky Way; the bottom node is Andromeda, the nearest big galaxy to us.

Giant intergalactic spiders, as far as we know, do not exist. But the cosmic web is still a “spiderweb” because of mathematics and geometry in nature. Similar kinds of structures appear in so many fields, linking biology, architecture, origami, geometry, engineering, and even the structure of the cosmos. 🕸