The Most Complicated Shape in the World

I love this example of one of the most complex shapes I can ever imagine because there’s a lot of depth to the form to unpack. Examples like this often work well for many audiences because each can choose their own level of interest. The many layers to the project can engage on multiple levels; one can appreciate its visual form, or study the deep science behind the shape’s development. Owning to my curious nature, I dive right in.

In the field of architecture, where spatial reasoning and spatial creativity are highly valued, studying the parameterization of the Wendelstien 7-X Stellarator and the resulting form sharpens our critical thinking and analytical skills to understand and produce such shapes in our the workplace. I find the shape of the Stellarator’s superconducting magnets sculptural and modern, and am deeply moved to know the form is primarily derived from natural forces. The final form of each magnet is so delicate, contemplative, and beautiful.

Finally, for me, the Stellarator represents the best results one could hope for from collaborative design. A single person could never have developed such a design. Expertise from multiple team members needed to come together. Applied mathematicians were needed to accurately model the plasma and magnetic fields; experimental physicists were needed to calculate out the exact forces at play and analyze the results; and finally, engineers were needed to build the thing safety. “If theses are the forces to be expected, how much bracing and structure is needed?”

To have a fuller understanding of the parameterization used, and why it takes collaborative design to achieve such a complex shape, we take a quick detour to the science of fusion energy. We only glance at the the topic — this being an architectural blog we’ve already strayed pretty far from our original subject to study a complex form — but something must be said of its fusion energy’s characteristics because they strongly inform the variables and parameters chosen for the design. Fusing the nucleuses of two atoms takes extreme heat and pressure. This is done in the lab using very strong magnetic fields. Earlier fusion reactor designs used the shape of a torus, called a tokamak, which mimics the shape of magnetic fields in nature. An illustration of the design can be found below (left) by the Joint European Torus housed in Oxfordshire, UK. The images don’t give a good impression of the large scale of the reactors, far taller than a person.

The Germans have been much more ambitious with their design. The stellarator (right) is just as big, and shares some similarities with a tokamak in that it’s also torus-shaped (with a hole in the middle like a donut). But those who love math will immediately notice an important difference. The plasma of the 7-X is kinked and folded and sort of looped over itself five times. This behaviour for this is predicted by generalized knot-theory where such patterns are studied. As to why it’s a more efficient design, I turn to the analogy of wringing a wet towel.

The design of the tokamak is much like trying to squeeze water out of a towel with only compression. We all learn at a young age it’s much more effective to twist the rag to get as much water out as possible. This is in effect what the stellarator is doing at the points of inflection; that twisting motion inherent in the design drastically increases the pressure which can be applied to fusing nucleasus, which in turn — in theory — should release more energy than put in.

Scientists don’t use abstract knot theory to model these fields because they’re not accurate enough in reality. Knot Theory only suggests its shape. Actually calculating out what forces to expect draws upon collaborative design to complete. Computational fluid dynamics play a major role in modeling, firstly, the plasma, and second, the magnetic field. Once the the shape,form, and density, of the plasma needed to fuse nuclei is known, then it’s a matter of parameterizing the magnetic field with the require magnets to generate it.

This scientific process results in those wonderfully serpentine-shaped magnets, which should probably be more accurately described as super-cooled, superconducting magnets. It’s the only way to generate magnetic fields strong enough. The alienform of the magnets are required to curl the plasma under itself. The design specifies 50 curved and 20 planer magnets to generate the required field strength and shape. The 50 curved magnets represent an incredibly complex shape, even their cross-sectional profile adjusts as they encircle the plasma. And yet I find them uncannily sculptural, ready to be discovered in a modern art museum. And all the time I return to the idea all they are is a model of Nature. Just another element in the universe.

Click for full size. Credit:reddit

The images included in this post barely do the form justice. Each ring is individually gorgeous, and I wish I could walk around them in a gallery to get a feel for their full spatial effects. To get a better idea of what these objects are like in 3D, I encourage readers to check out the video attached to this post. Hopefully it will give a better sense of what kind of 3D space these objects create.

— — — — — — — — —

Blair Birdsell is a design technologist in Vancouver, B.C. Please feel free to follow connect on LinkedIn for more long-form pieces about digital design and sustainability, or on Instagram for a full-throated celebration of architecture.

The Perfect Architecture Company. Design, Engineering, 3D Printing, Sustainability, and BIM.