I guess this would be called Prototype Zero because I never intended to use the Geomancy Lantern as an architectural model. At some point I was staring at the structure and realized that the geometry culminated into square brackets that could perfectly accommodate standard 4’x8′ sheets of material. Using unaltered building materials had always been a goal of this project, I just wasn’t quite sure how this could be accomplished till I had the revelation.

# The Begining

In 2009 I received a grant from Kansas City based Avenue of the Arts. I had proposed a piece of public art that would be a glowing crystalline melting landscape that was based on previous explorations in traditional landscape painting. I was searching for a structure to accommodate the elements of landscape and I settled on the tetrahedron. I quickly became interested in fractal tetrahedrons. Essentially the 3d version of this:

### Considering 3d Space

Two points make a line. Three points placed equidistant make an equilateral triangle. If you extend this surface you get a plane. Four points placed equidistant make a tetrahedron. If extended, create volume. 3d space as we know it. I’m not sure why 4 points are considered 3 dimensions but this boils down to semantics. What is a dimension? A point exists in no dimension? A line exists in the first dimension? Paper is paper thin, but its still technically an object in space with real, albeit minute, depth. Points, lines, and planes are theoretical objects that could never be seen by human eyes. I think classic geometry has some things to work out.

When Considering models of the universe the theoreticians are always on the hunt for elegance. A clunky model does not reflect the language of god. It’s really hard to explain the motion of planets if the sun isn’t the center of your model. It gets baroque, b-roke, clunky. The pieces fit better and Newtonian physics makes way more sense when the Sun is in the center. Triangles are the most primary 2d (classic 2d) shape. Tetrahedrons are the first and primary voluminous shape. How did we get started using classic grids of squares?

Try to speak a poem with as few words as possible. Verbose English majors usually don’t make very good poets. The universe is poetic, and your basic module for dissecting space becomes important when trying to coordinate objects in space. Remember doing trigonometry on a Euclidean grid? It always produces inelegant ongoing decimals. A base-ten numeric system can’t very well represent pi, or even one third (.3333333333333333333333). This could all be considered evidence that our basic tenants of mathy phenomenology were just band-aids; band-aids now soaked in stars.

Shannon’s information theory illuminates certain rules that we can maybe abide by. It was designed in the zone of human subjectivity but rigorously attempted to quantify the quality of information with mathematical models. It’s a heavy subject but we can maybe deduce that conservation of information is universal. Poetic concision is universal. Any creature looking to transmit data will try to express it as concisely as possible. This concise formatting will probably be more consistent with the raw functionality of the universe. I’m no mathematician but I have this feeling that expressing coordinates in space is way more concise using a tetrahedral lattice instead of a Euclidean grid. The fractal tetrahedron is pretty interesting too because it parodies Shannon’s work. Shannon said that every time you transmitted a bit, you would halve infinite…a logarithmic reduction of ignorance with every piece of information transmitted. He figured out that the best way to measure information is by its negative space. So strange.

Coordinating in fractal tetrahedral lattice space? You could draw a line from here to the edge of the known universe, then cut it in half. The first bit transmitted tells the other entity what side of the division you’re on. The second bit then divides that space and provides an even more accurate location…and so on. Can this be done on a tetrahedral lattice? I’m still thinking about it.

### Modeling

So instead of worrying too much about quantum physics I just started building, finding ways to create a fractal tetrahedral building module to fill out space and provide a surface for my landscape.

You can see the notches at the mid point of every line. This is where smaller tetrahedrons are mounted. This is the 24″ module cut from 1/2″ OSB. The smaller on is 12″ cut from 1/4″ Sintra. The next fractal iteration would be cut from 1/8″ material, and so on.

Above, is what happened when I applied these concepts to architecture. You can see some areas I use smaller tetrahedrons to add more detailed space. Kind of like a 3d pixel; or how jpg compression works. The large swatches of color use less data, and data is added where its needed around detailed regions. This method is nice because the tetrahedron has what is called vector equilibrium. All points are equidistant. With a real object, a point or node represents functionality. In it’s simplest form, architecture is just sticking sticks together. Most building materials are either sticks or squares. Its actually really simple. Considering human will in a structure, you never know where you might need an element of functionality, so vector equilibrium in a primary volumetric shape is the most concise way of covering your bases. In this example the smaller fractal iterations always mount at the midpoints of the larger. These ideas have been carried into more advanced versions of TetraHouse. This was the first stage of conceptual development.

## Geomancy Lantern

All projects get cut short by the real world. For the final install of Geomancy Lantern I wasn’t able to implement different scales of tetrahedra but aesthetically everything looked fine so I rolled forward.

Here I am wiring the lights up. Tetrahdrons work great for light boxes because every node has an adjacent face that roughly fits the projection angle of and LED. I used Ethernet cable which is really cheap. I used some dirt cheap Ethernet couplers to plug the modules in. Ethernet has 8 internal wires which is also perfect for the four LEDs in each tetrahedron. The gauge of the wire ended being too small and half my amperage was burned off in the wire’s resistance. An 800 watt power supply was only able to power 400 watts of lights. Bummer.

The pictures are taken from an epic wilderness hike. I was in psychedelic mode, and walked 30 miles in one day only eating a handful of granola. I snapped off 2000 pictures. I saw 100 head of elk plowing across high plateau with gold mist rising all around. Deep blue pools and neon lichens. The photo set was later expanded to near 10,000 using some After Effects tricks. These were then sifted and reduced in rapid fire based on their colors, textures and compositions. The fractal theory worked out pretty well for the printing process. I did end up print two different scales of triangles which created very little waste in the print layout. The bigger triangles filled out bigger space, the smaller ones filled in the gaps. A million dollar CNC knife cut the whole thing down into piece pretty quick.