In 1917, artist Marcel Duchamp labeled a urinal a fountain, as he changed its context from a bathroom to a museum. In this experiment, the role of a vault changes from a global geometric logic to a module for a volume packing structure. The orientation of a vault is normally critical to the structural performance of the catenary curves which define it. In this study, the vault’s specific geometry no longer performs structurally, and instead functions perceptually in an unprecedented manner. As the vaults rotate around a common centroid, the outer boundary becomes redefined with what appears to be quills or spikes, while the inner boundary becomes defined by pillow-like curvatures.

The definition of boundaries, conventionally a constraint, is a design opportunity in this case. Both the inner and outer boundaries defined by vaults could extend to frame more than one shape. The outer boundary no longer has to be an offset of the inner. In one study, the inner boundary is defined by a sphere while the outer boundary is defined by a cube. The geometry begins to have the illusion of material thickness as it mediates between two boundary conditions, creating a spatial depth within the geometry’s boundaries. Definitions of geometry, boundary and texture become blurred in this study.

Often times, designers begin to work within a given medium without explicitly acknowledging how embedded constraints will influence their design process. The experience and consequences associated with digital instrumentation will yield different results than those emerging out of physical material manipulations. A digitally driven design may be seamlessly precise and consistent but may also feel sterile and distant from the human body. A materially driven design may be intimate and tactile but may lack the accuracy needed to connect elements. This experimentation combines digital fabrication techniques with hand craft material manipulations in search of a unique hybrid tectonic that merges connection accuracies with subtle but sensual divergences between repeating modules. The challenges associated with translating a consistent material process over each scale have become explicit within this research.

This research does not claim to have developed a "better" fabrication process, but rather asks the question, how do we qualify fabrication processes in our current discourse? A hybrid fabrication process which combines digital fabrication with hand craft techniques suggests an alternative approach to current fabrication trends; automation and optimization. Perhaps, a slightly slower process which yields a sensibility to intimacy is something to be considered.

A shape could be defined symbolically, like a specific platonic solid, or a shape could be examined through the lens of plasticity, in which all shapes are considered interconnected and related. Assuming that shapes are plastic, it is possible to transform one shape into another. While manipulating a tool which allows a shape to be altered, it is often possible to predict and visualize the result of a particular transformation. However, it is not as easy to imagine the result of a three dimensional geometry mapped into a two dimensional world. Mapping transformations are often more difficult to visualize.

This investigation focuses its concentration on transformations of polyhedra to their respective flattened edge unfolding. When a shape transforms, how does its unfolding pattern transform? In 1975, Geoffrey C. Shephard posed the question, "Does every 3-polytope possess a net?" This problem still remains open to solve. This research does not attempt to make an ultimate proof, but rather attempts to develop an intuitive correlation between these two worlds. The first study in this line of inquiry initiates a mapping dialogue between a geodesic dome to a "textured" dome.

Most software uses a linear hierarchical structure, building each rule or logic off of one another. Such linear structures can become extremely specific and fixed to the point where they are only able to compute one task. As soon as a designer wants to change the computed task, they have to redefine the entire input structure. In the mathematical model, all modes of transformations and flexibility are under one systematic language. The designer never has to redefine the initial structure of the system; the designer has to simply alter within that system. Since mathematical models are based on a global Cartesian coordinate system, the designer can at anytime alter the computational hierarchy and embedded as they like. Designers can begin to think and manipulate in a less linear fashion and constantly redefine the "world" within they create and perceive. Like throwing paint onto a blank canvas, the Cartesian coordinate system becomes that canvas!

Nothing ever has to stay completely fixed within mathematics, even something like a curve! A curve may be a curve but a curve could also become a tube or space. Anything imagined could be embedded inside another shape. In this experiment a space is literally thrown on top of another space; a "world" in another "world." Algebraically one "world" can transform while maintaining the other’s parameters. The local and global orders are defined under one parametric equation, rather than defined by linear hierarchical layers.

When mass is lifted on Earth, our body undergoes suffering because of the weight of gravity. Gravity pulls down on our body. Feeling forces acting on us. Similarly, when a ball of clay lies in the palm of a hand, the clay has a mass; our hand is its boundary, its cage. If the hand squeezes against the ball of clay, the ball distorts because of weight of forces acting on it. This experiment begins by applying computational weights to a sphere defined by weaving. The sphere distorts based on the weight and direction of the forces acting on it. Physically the distorted woven sphere is constructed identical to the virtual model. The physical model’s shape is not derived by weights acting on it, but rather is the result of the digital distortion. Linear lengths in the computer are recorded to constrain how the shape is physically constructed out of linear tubing. The woven shape maintains the same curvature distortion as the digital representation.

In this instance, the physical manifestation has become nothing more than an instrumentation or recording of that which has been designed in the virtual. At what point are opportunities lost by not re-envisioning a project through another medium? When is it acceptable to stop designing and start recording? Is it ever acceptable?

Inflexion is a point on a curve in which the curvature changes sign. Like wind eroding sand dunes, its geometry is the result of outside forces acting upon it. In a field condition, it is possible to register forces by perceiving changes in repetition. Rather than manipulating a global geometry, this experiment manipulates local texture globally. Each mound incrementally deforms, such that the mounds do not read individually but as a collective, holistically following a common curve attracting their orientation.

"Metaphorical references to inflection, wind, and erosion are important to this artist’s interventionist mark making. Inflexion would be an elegant scar on the surface of the earth that recalls the land-based practices of Dennis Oppenheim, Robert Morris, and Robert Smithson. Inflexion refers to the power of man to effect change, while suggesting that such alteration is also subject to natural forces beyond human control." -Ann Wolfe, Curator of Exhibitions and Collections, Nevada Museum of Art

In the 1800’s, Joseph Fourier attempted to prove that every shape could be described by trigonometric functions. Fourier’s proof was close to perfection, except it ran into difficulty modeling square curves; curves constructed of zero curvature joined perpendicular to one another. This research does not attempt to make an ultimate proof, but rather attempts to find the rules and logics behind trigonometry’s transformations that would allow anyone to manipulate the algorithm in an instrumental manner rather a purely deterministic one.

Potentially, all shapes can be defined with the trigonometric transformations of sine and cosine. This research is the first to define the eleven most fundamental types of trigonometric transformations: cutting, scaling, modulating, ascending, spiraling, texturing, bending, pinching, flattening, containing and thickening. By combining these eleven transformations in different hierarchical manners, it is possible to generate any shape imaginable.

Spheres, cylinders, and cubes are a small handful of plutonic shapes which can be described by a single word. However, most shapes cannot be found in the dictionary. When a designer designs, would a designer prefer to design with the relatively few shapes found in the dictionary or all the possible shapes in the world? Many contemporary digital tools use a fixed symbolic interface, similar to that of the dictionary. When a designer wants to create a sphere, the designer clicks on the icon and draws a radius. If a shape is defined by a single symbol, all the designer can do is manipulating the matter of that shape. Like a ball of clay, the sphere can be stretched, twisted, pulled and cut. If the sphere was defined by a parametric equation, it becomes defined by a ruled based logic that contains parts smaller than it.

By manipulating the shape’s "DNA" or trigonometry, it becomes clear that there is a new range of geometric freedom that could not have been imagined in the other "world." Since the smallest morphemes themselves are being altered, understanding how each function influences a particular transformation becomes obvious. In this experiment a sphere is peeled apart, twisted, and looped around itself. It is only possible to transform a sphere in this manner because of the periodic nature of mathematics.

A machine will always be able to record and calculate better than man can ever, but a machine will never be able to wander as well as we do. It is imperative to think of these mechanisms not purely as deterministic. Even within mathematical models which get to the most fundamental building blocks of the computational engines there is the simple logic of an input and an output. This logic alone is not design! It will calculate for us, but we need to intervene, and constantly transform the algorithm or "world" at hand, according to criteria which we identify during the process. We are the feedback loop, and without us, it’s just automation.

By playing with algorithms it is also possible that the initial lack of control could help generate unpredictable shapes that may guide the design process in a new direction. Instrumentalizing is not simply about memorizing specific rules, but rather also about developing sensitivity and intuitive understanding of the medium. Like any medium, it can only be truly learned by doing. This experimentation goes back and forth between tacit experimentation and explicit learning. The Classic Klein Bottle becomes the test specimen in this exploration. It is discovered that by adding additional elements to a base mathematical equation, the topological continuity of that shape is maintained. The number of openings is varied globally; while locally multiple transformations are combined to sculpt a more dynamic form.

What is space? In architecture, space is defined by metrics of areas and volume in an enclosed container. A dancer would define space based on the movement and reach of their body. How might wind define space? Can space be defined based on the movement of outside forces?

Everything is considered to have matter; even air has atoms and particles which have mass. Rather than defining space based on fixed boundaries such as walls or surface, why not define space in a less totalitarian manner? In this experiment, a field of hairs become like particles in air. As an outside force acts on them, they transform and lean. As they lean incrementally, the once ordered Cartesian grid begins to distort. Zones of expansion and compression evolve, defining an ambiguous space of inhabitation. When the outside forces have moved on, the space disintegrates, as the condition returns back to its natural stable, relaxed condition; a space with no hierarchy, therefore a non-space. Perhaps space can only be defined in environments of instability.

A tool is a device that augments an individual’s ability to perform a particular task. The more specificity a tool has, the narrower its instrumentality. Tools inherently constrain the way individuals design; however, designers are often unaware of their influence and bias. Digital tools are becoming increasingly complex and filled with hierarchical symbolic heuristics, creating a black box in which designers do not understand what is "under the hood" of the tools they drive. And yet designers are becoming fascinated with engineering mentalities: optimization and automation. Simply, it gives a solution. But, this is not design! Designers need to work outside of a fixed atmosphere!

The future of digital instruments is not more complex heuristics, but rather the contrary. It is imperative to go back to the most basic building blocks of these "engines:" mathematics. Within mathematics, functions can be embedded inside other functions at anytime, giving designers endless freedom to alter the computational hierarchy. In this experiment, the boundary of one shape is completely altered to the confines of another shape by simply placing its mathematical definition within the others. The complete hierarchy is transformed while maintaining a consistent framework and parametric equation.