# Nuclear Thresholds

## Architectural implications of Enrico Fermi's Chicago Pile-1

### Zoë Prillinger, Luke Ogrydziak

We were asked last winter to think about making a commemorative installation for 75th anniversary of Fermi’s “Chicago Pile-1”, to be entitled Nuclear Thresholds (fig. 1). The project brief invited us to reflect on the nature of Fermi’s experiment, as well as the tension between control and the loss of control engendered by the birth of the Nuclear Age. In developing the project, we thought about chain reactions, and the random walks of liberated neutrons. We thought about critical mass, when a chain reaction is barely self-sustaining – such as was the case with Fermi’s experiment, and supercriticality, the turning point when the rate of fission increases, sometimes to the point of being out of control. We were interested in the complex materiality embodied in the original experiment: the tightly-packed pile of graphite used for the experiment, as well as thinking about matter as something not solid but composed largely of space and energetic particles.

The project was very open-ended, functionally speaking. We knew the installation would share space on an existing plinth dominated by a large bronze sculpture by Henry Moore. Moore’s “Atom Piece” was installed to mark the commemoration of the 25th anniversary of Fermi’s experiment. We were asked to consider how the installation might enhance the viewing Moore’s sculpture at the same time that it reflected on the original physics achievement.

## 1 Genealogy of ideas

To describe the evolution of our proposal, and create a broader context for the architectural issues involved, it is helpful to situate it within earlier research and built work that is fundamental to some of the basic ideas. A critical theme is the idea of control, and loss of control. Architects typically like to be in control, in fact, that is one of the ways one typically judges the success of a project: did what the architect want to happen happen? The more control one can exert to manifest one’s vision, the better architect one is. In architecture, this can mean the control and management of space, the control of form, the control of behavior, and the control of experience. Architects tend to be real control freaks. It can be especially difficult for this kind of individual to come to terms with a loss of control! All the more reason for architecture to come to terms with this trauma.

When we talk about the control and the organization of space, it is impossible not to think of the grid, efficiency, and close-packing. The ideal in all these highly rational approaches is no wasted space. If you think about close-packing, there are some basic geometric alternatives to the grid that can efficiently tile space without any gaps (fig. 2). The stacking of basic prisms is highly ordered and very repetitive.

But our office is excited about some level of unpredictability. So, some years ago, when we were doing a project based on close-packing, we learned about the Conway biprism (fig. 3). This is another prism which tiles space perfectly (with no gaps). But in this case the resulting layers are rotated a non-repetitive angle relative to all the other layers, giving us a system spawned by a single object that extends to infinity without repetition. We conceptualized a world governed by this system, and within it designed Conway House.

Just as we were excited by the irrationality of the tiling of Conway biprism, we started to look for other ways to free ourselves from the confines of perfect efficiency. We started to explore inefficient packing. Tetrastars (fig. 4) again starts with a simple unit that is repeated. But here the overall system is created by stochastic aggregation rather than a geometric rule. The order is statistical and timebased rather than purely geometric.

Far along the spectrum of unusual assignments, we were asked to work for a hypothetical gopher client for an art installation in the San Francisco Presidio. In the gopher we found our perfect client because these creatures combine a high degree of spatial efficiency in their tireless digging with a solitary nature that avoids adjacent gopher burrows. We designed a Processing program that propagated multiple gopher agents who incrementally filled space with their branching burrows using buffered collision detection. Burrows (fig. 5) combines a high degree of density with stochastic development. We used the branching plans for a planting arrangement of the native forbs and grasses that gophers prefer to eat (as they burrow in underground safety).

In Branch (fig. 6), we explored the same issues volumetrically. Branch begins with a seed point that branches outwards in all directions stochastically, again using buffered collision-detection. The result is an aggregation that is pretty tight, but because of some inefficiencies born of randomness, it is also very complex, and to our mind, spatially exciting.

Also time-based, we generated the façade of Gallery House (fig. 7) stochastically, using a simulation that uses self-avoidance to create an organic lattice. The agents were constrained within an envelope determined by the allowable projection from the building face. In San Francisco, this allowable projection is the reason for the preponderancy of bay windows, but here, combined with the blind stochastic nature of the simulation, it results in a much more organic, undulating volume.

So, you can see with all these strategies exploring stochastics and inefficiency, we are looking for a way to set something in motion that surprises us. Swirling is another strategy that we think is exciting for related reasons. Swirling takes us more deliberately into thinking about the opportunities that architecture has to create psychological effects in the user. Leonardo da Vinci’s 16th century studies of water turbulence demonstrate a Renaissance fascination with complex, dynamic formal systems. Clearly, this is not a new interest! Swirling creates situations that are hard to predict and control. The swirling effect is something we are interested in exploring in our work at all scales of form and surface. We like it because it challenges a dominant organization of space – orthogonal geometries, in the case of architecture.

About ten years ago, in thinking about swirling, we designed a C++ simulation of a bee’s flight path. The looping, relaxed tendrils, and wandering curves of different speeds were intended to be used for the decorative relief of a ceiling that was never enacted. Shortly after, we started looking again at the looseness and freedom in the painter Brice Marden’s Cold Mountain series. In particular, we liked the tension between the freedom of the curves and the constraint of the edge of the canvas. We analyzed the qualities of the Cold Mountain curves (fig. 8), and created a machine that could enact the same genre of looping.

We adapted this research for another project, but in this case wanted meandering paths to wander three-dimensionally for a set period of time (fig. 9). One of the interesting challenges in Timeout/Temps Mort, as in the Cold Mountain piece, is the tension between freedom and constraint (fig. 9). In this case, the freedom of the curving paths is constrained by a virtual bounding box and by self-avoidance.

We developed a Knot Machine to explore similar themes but endowed the agents with a greater variety of behaviors, ranging from straight lines to tight curves (fig. 10). Additionally, the agents could be attracted to points, or sucked into vortices.

Recently we had the opportunity to apply a vortex to a built project (fig. 11). In Vortex, we positioned a mini-vortex at the front door. The resulting faceted geometry reacts to the tight winding and relaxes as it flows out in different trajectories.

In a recently completed project called Shapeshifter, the swirling happens at a larger scale, informing the development of the overall form and the movement that it implies in both landforms and architecture (fig. 12).

All of these explorations were hovering in the background when we began to think about the Chicago Pile-1 installation. We started by learning about the original experiment –both the site, and the physics involved– and developed some preliminary models. These were not yet specific proposals, but rather specific formal systems related to the issues we were considering.

## 2 Initial approaches

This first model began with the idea of close packing spheres in a time-based diffusion-limited aggregation (DLA) in which the spheres were confined within a hexagonal array (fig. 13). The CP1 experiment took place in a disused squash court under the University of Chicago football stadium, so throughout our research on nuclear processes there was a ghostly presence of squash balls. Indeed, to our literal-minded eyes, there is even an uncanny formal affinity between the perfect circles and spheres of physics diagrams and the humble squash ball. Initially we wondered if the installation might be made aggregated squash balls. But if you do the math determining how many squash balls it would take to fill a one-meter box, it is quite surprising. Well, perhaps not to a mathematician or a physicist. But we were surprised: we could blow our entire budget on a tightly-packed 1-meter cube. Precisely our surprise made us feel like this could be interesting territory. Could the project start with an area of close packing (of spheres) which then was dispersed with greater porosity and less homogeneity? Ultimately, our final project incorporates elements of this first model, albeit in 2 rather than 3 dimensions – much more economical! In the original CP1 experiment, the particles moved through the graphite blocks of the pile in “random walks”. Diffusion-limited aggregation (DLA) simulates random walks, but instead of solidifying the path of a single agent, we released multiple random walking agents at the edge of the model, and wherever they hit, the model grew (fig. 14). We also translated the resulting hexagonal array into a planar mesh, then “relaxing” it for a more organic morphology. This approach yielded some interesting spatial complexity, but ultimately felt too uniform and homogenous. We were looking for a system that had a sharper internal break, that was somehow articulate about the existentially pivotal moment of the CP1 experiment and the idea of the criticality threshold. This simulation felt closer because of the sudden exponential growth. But unlike an explosion, our installation would necessarily be a static form. In other words, the development of the system over time would need to be implied rather than enacted – a common architectural conundrum in the digital age.

Then suddenly in the spring, the project went from a kind of hazy possibility to having a greenlight and a working budget. So we switched gears from more abstract research to specific proposals for the actual site. A sketch from our initial concept discussions (fig. 15), made before we even started the computational research, goes to show that one just cannot fight one’s unconscious.

In our initial design pitch to the University, we presented two possible schemes. The winner involved layering rubber tubes of variable density to create a bench of tightly-packed strands which hits a “threshold” and increases in complexity. The development of the project combined material research, and the creation of both physical and computational models, all of which influenced each other in non-linear ways.

A basic chain reaction diagram helped us visualize our thinking (fig. 16). We felt that focusing on the exponential growth of a chain reaction was a promising way to manifest the complexity. As architects, we also wanted to challenge the model of solidity that we all rather stupidly work with, with an updated model that considers matter on a subatomic scale. Ultimately, this would come to mean contrasting a coherent, organized “solid form” with a breakdown into atomized independent parts.

The diagram shown in fig. 17 illustrates in what would ultimately become the model for our project: one unified group splits recursively until the constituent parts are all independent.

## 3 The realities of construction

The original CP1 experiment was conducted using a tightly-packed pile of graphite blocks. For our installation, we incorporated a similar strategy of highly efficient piling for the region of greatest density. A drawing of the tightly-packed part of the installation, the bench, illustrates the stacking of 241 x 2${}^{\prime\prime}$ diameter cords. The cords are arranged in a hexagonal grid which is the 2-dimensional equivalent of our early 3-dimensional hex-grid study models. It is as if the original squash balls studies were extruded into strands. Rather than just cutting a vertical section, the bench arc begins with a single strand (fig. 18). We were trying to emphasize the process of piling, and also how the apparently solid form is composed of individual strands with their own autonomy. We found it interesting how following an extremely simple rule for piling (based on uniform offset) created a complex sheared and curved form simply because of the embedded complexity of combining concentric curves and the hex-grid section. The specific result emerges from a process enacted strand by strand rather than a classical top-down approach.

Because of the complexity of the model, conventional strategies of representation simply fell apart. Most architecture remains based on boxes. Walls, floor, and roofs are all rectangular prisms composed of various material laminations. In turn, these rectangular prisms form larger hollow rectangular prisms that can be occupied. The occasional cranked plan or section does little to disturb this model of matter as fundamentally solid. To model a form that gradually disintegrates triggered some new work flows, and also an acceptance of the inevitable gaps which would emerge between the representations and the thing itself. In our first physical study models, we used black licorice and thread for the bundling. The tendency for the licorice to slump provided a pretty good approximation of the character of the final piece. This model was really useful for studying the possibilities for the bifurcations, and establishing a language for the curves at the area of the splitting.

In the middle of the summer, things seemed to be going really well. Our study models were progressing nicely, we were well under budget, and had found a local Chicago supplier. Then the 1:1 samples arrived and everything fell apart. We had been hoping to use 4${}^{\prime\prime}$ diameter rubber tubes rather than solid strands to reduce the overall material quantity. But the tubes all had technical issues which made them unsuitable for the application. They were either too rigid (to compensate for being hollow) or too flexible (because they were hollow). Our solution was to use solid 2${}^{\prime\prime}$ diameter solid EPDM rubber cords. This was the largest diameter that would still have the flexibility we wanted for the piece at full scale. Our typical section is a hexagonal grid, with the interval based on the diameter of the cords. Because area was a function of length times width, this switch effectively quadrupled our strand count – creating more much work for the installation downstream.

With these new parameters, we could no longer source appropriate licorice. So, we had the new issue of making a larger study model which would approximate the behavior of the 1:1 cords – an impossible task because physical characteristics do not scale like this. Ultimately, we opted for Buna rubber for the final study model. It was important for us to have a live study model on site both to convey the design intent to the fabrication team and to “react” to the situation in real time.

Concurrent with the physical models, we developed a series of digital models as well. These were all physics simulations which used the open source Bullet physics engine (fig. 19). We learned a lot about both the joys and pains of physics simulations. At 64 strands the model was actually pretty friendly to build and use. But the primary issue was actually trying to animate the design process itself. E.g., grabbing a cord, twisting it, tying a knot, etc. Because the Bullet engine focuses primarily on collision detection, we were somewhat forced to design using gravity and impacts. So, for instance, we might drop or slide our model, and hit it with something to wrap it around a cylinder. The results were certainly stochastic and unpredictable, and in many ways fascinating. But they tended to strongly privilege certain setups over others, and not always the ones we wanted.

To address these limitations, we also developed an Inverse Kinematics (IK) model (fig. 20). This was essentially a poseable armature representing our strands. In many ways, this had the opposite problem of the physics simulation. We had total control of how to position each joint, and could develop upstream dependencies. But we had lost the automated collision detection and also the “automatic” aspect. Instead of a simulation we were developing a character model. Furthermore, in the middle of this process, we switched from 64 to 241 strands. Our digital models needed to be rebuilt, and everything needed to be automated because of the increased complexity. Just like actual installation, on the computer the “bundling” of the strands is what really took time. Interestingly, total freedom for the strands was trivial to setup.

In early September, the strands arrived in Chicago and we flew out for the installation, where our concerns immediately became full-scale. Each EPDM cord weighed approximately 120 pounds. And the glass library dome is pretty reflective in late summer, so it was a laborious, tactile experience. All the connections were made with UV-resistant zip-ties. Ultimately, our installation process paralleled the steps of building the physical model. However, after the fabrication experience, it is hard to imagine being able to accurately simulate the physicality of the actual strands in any alternative medium or scale.

In terms of the specific morphology of the tangle, there were a variety of considerations. We wanted the first split to be extremely dramatic. In our study models, we preferred for this split to be horizontal, and for the top to flop over itself, creating a wavelike form. This is a very heavy bundle, so this is something that had to be planned out before we finished the bench arc. Slightly downstream, we wanted areas that were as high as the bench arc, and that also had a feeling of swirling around a local center. There is the implication of a local attractor of variable intensity which pulls the strands around itself. One tension was keeping the stranding legible, without having the overall gestalt be too tree-like. We wanted a slightly malevolent feeling in keeping with the idea of our own ambivalence about the nuclear threshold that was momentously breached 75 years ago by Fermi and his team.

As an intervention on the site of the original experiment, the project implies a protean pile of material that begins as a simple arc and then dissolves into exponential complexity (fig. 21). It pays homage to the Henry Moore’s Nuclear Energy by intensifying the site and partially enframing the sculpture on its vast plinth. The bench invites contemplation and directs focus to the Moore before it bifurcates into a tangled landscape background. An organized, seemingly solid form fragments into wild incoherence.

The cords are close-packed in a hexagonal array, forming a simple arc that serves as a bench (fig. 22). After forming a quarter of circle, the form splits into two branches that explode the regular, controlled form of the arc. Those two branches then each twist and split into two more branches, and so on, exponentially increasing the complexity of the overall form until all the cords are writhing freely.

## 4 Final considerations

When we were initially conceptualizing the project, it was important that the installation had a perceptual ambiguity, that is to say, two inseparable natures. This duality became a fundamental quality of the installation. From certain initial vantage points, for example, as you approach the plinth, or view the Moore head on from the street, the curving, form is simple and Platonic – essentially a truncated cone. This region identifies with a classical, centered space, the realm of dutiful reflection (fig. 23).

But as you traverse the plinth, the form becomes restless and incoherent. The swirling induces a loss of orientation and an immersion that undermines modern notions of clarity and order. Architecturally speaking, we are excited about both models, but believe that swirling presents an opportunity for critical architecture to challenge many of the normative conditions and received ideas embedded in the world as typically constructed. Swirling space, however disturbing, may ultimately be a more accurate representation of our current world. In this installation, we were able to expand our extended interest in looping and tendrils, as well as in an energy born of intertwining and abrupt changes in direction. This model of space and form calls for an adventurous spirit, but it seems like an inevitable exploration is due since the classical model is pretty exhausted (fig. 24).

This view exposes the initial bifurcation and breakdown from clear form to wildness (fig. 25). After the rupture, the coherent form of the arcing bench collapses into an amorphous swirl. The form as it breaks down and intensifies as successive branching erupts into loops, tendrils and knots. We were thinking about random behavior, and during fabrication looked to the heavy, dense, incredibly supple material to suggest its own wayward path. We were excited about the chaotic zone of the project, and anticipated that the free-form landscape would suggest all sorts of explorations and liberated uses to passerby. But we observed that people tend to prefer to occupy the safety and prescription of the bench. By the time most people become adults, they have been socialized to sit on a bench, and recognize its use – they have swallowed the lessons and conventions of public space and internalized them as acceptable ways to participate in society.

Fortunately, we witnessed a kindergarten outing that unleashed the right kind of fearless civilians on the site. We started to see exactly the kind of play and acceptance of incoherence that we hoped to provoke (fig. 26).

The space of swirling and complexity, that is to say, the challenge and the promise of Nuclear Thresholds, is rife with peril and potential. We are now in an era which cannot unknow what it knows and revert to simpler times. According to the ancient Greeks, the three Furies would pursue and destroy mortals who had committed hubris by overstepping their limits, or crimes against the natural order (fig. 27).

In fear, the Greeks referred to them as the “Eumenides” – “The Kindly Ones”, rather than their true name the “Erinyes” – “The Vengeful Ones”, hoping that sweet talk would soften them.

However, now we are fully entangled, and neither flattery nor turning away will make a difference. Perhaps we need to take a lesson from the intrepid explorers and learn to make ourselves at home in this restless space – to make the best of it (fig. 28).