WORDS

UNDERLYING STRUCTURES (from Christine's book)

I am interested in the origins of creation; how things come together, how they fall apart and the emergent qualities of those interactions are the motivating factor in my art practice. Being acutely aware of pattern early in life initially led me to graphic design. My 20-year career working as a designer frequently involved designing patterns for various clients. Prior to 2011, my paintings were heavily patterned, but there was always something problematic about the repetitive mark-making in my work. Looking back, I know that I was searching for complexity by creating complication, but discovered that layering patterns didn’t offer me the results I was after. The solution was in finding the right pattern. I began researching a variety of patterns and came across a unique pattern that does not repeat, called the Penrose pattern [figure 1]. The distinctive property of aperiodicy in this pattern has fascinating connections to a variety of disciplines such as sacred geometry, theoretical physics and chemistry. Employing the Penrose pattern led me to rethink the origins of creation as well as the underlying structures that make up our reality.

Painting left me feeling confined by the edges of the canvas. The periodic repetition in my work would always infer an endlessness, but ultimately stop at the edge. The non-repeating Penrose pattern is different in that there is no defined edge. At first glance the Penrose looks as though it’s an ordinary repeating pattern, but upon a closer inspection, there is no repetition. It is the repetition of difference not the repetition of sameness. Based on five-point symmetry that completely tiles a plane with no gaps using only two rhomb shapes, there is never an absolute end. The tessellation rules for the Penrose are rather complex in that you cannot really predict with any certainty where the next tile goes outside of a local area. In my early installations, I used string [figure 2] to engage the space and bring the rhombs out of their two-dimensional domain. Although I was successful in giving volume to the rhombs, I was frustrated by my lack of ability to tessellate the Penrose in 3D using two rhombs. This led me down the rabbit hole of theoretical physics, chemistry and geometry in my quest for a solution. I discovered that much like seeing a 2D shadow of a 3D cube, we know that the cube is 3D. The Penrose in 2D is a projection of a 4D structure. What had I gotten myself into? I failed algebra in high school and was feeling like I was in over my head.

My practice takes cues from the long history of art being influenced by science, and even more specifically, the study of the 4th dimension. In the late 19th and early 20th century, there was quite a bit of work done in mathematics relating to the existence of other dimensions. In 1908, Hermann Minkowski presented a paper about the 4th dimension on which Einstein later based his theories of relativity. The study of the 4th dimension coupled with a long string of other significant scientific discoveries such as x-rays, electrons and radioactivity led to a rapid change in the world view of reality. Before these discoveries, the 19th century impressionists were consumed with light and shadow that could be seen with the naked eye. In contrast, the cubists were inspired by the invisible world revealed by the revelations of the science of their day. Mathematician Esprit Jouffret’s 1903 illustrations of hypercubes projecting from the 4th dimension were said to have been Picasso’s inspiration for cubism. Portrait of Ambroise Vollard (1910) [figure 3] seems to be the first work that demonstrates the shift in his painting after his exposure to 4th dimensional hypercube drawings. In 1912, Duchamp became so intrigued with the 4th dimension that he stopped painting for 9 months and took a job in a library where he devoted his time to the study of fourth dimensional and non-Euclidean geometries. Woman Descending the Staircase No. 2 [figure 4] is a good example of this influence.

Believers in sacred geometry see the self-symmetry in nature as cosmic significance of a divine order. Self-symmetry is an interesting aspect of non-periodic patterns in their self-reflective symmetry. At first glance the mirroring could be taken for repetition, but upon further inspection, there is a more subtle complexity. A good example of mirroring forms could be seen in Dororthea Rockburne’s show Drawing Which Makes Itself, 2013 at MOMA. While considering her long career in 2001, Rockburne writes, “In working with mathematics and geometry, I am trying to explore through art the very origins of creation… I found myself recently stating, much to my surprise, that in fact I’ve never made an abstract work of art — my work is about the unseen forces, which exist in a form of nature, which seeks to define substructure.”1 An underlying theme of Rockburne’s work is a variety of mathematical systems and theories including topology, set theory, the golden ratio and Fibonacci numbers. While a student at Black Mountain College in the 1950s, Rockburne was strongly influenced by mathematician Max Dehn. Dehn taught a class for artists on geometry as it exists in nature and how shapes interrelate to one another. Rockburne’s work reveals the symmetry of line and shape through various algorithms of marking surfaces and folding. She called out the non-repeating triangles by mirroring them in her folding technique. [figure 5] I find a substantial connection to Rockburne in my interest in substructures of aperiodic patterns and the unusual properties of self-symmetry that they possess. Unlike Rockburne, I believe what can come from aperiodic pattern has more potential to reveal the underlying structure of reality than the pattern itself. As it turns out, my journey also connected me to the origins of creation much like Rockburne’s explorations in her work. While I worked on Rotation 72º , I was concerned with calling attention to the non-repeating nature of the Penrose. I considered how Rockburne had used multiple triangles in a variety of proportions and angles without real repetition in her folding pieces. Finding the matching shapes in her work clarified a hidden set repetition. By removing the outlines of the Penrose rhombs I was able to hide the illusion of repetition and show clearly the non repetitive nature of the pattern by calling out the varying sets of tessellations.

The Penrose pattern was first discovered by mathematician and philosopher of science, Dr. Roger Penrose in the 1970s. He found that two rhomb shapes could completely tile a plane with no gaps and never repeat—a major mathematical breakthrough. In the 1980s, Dr. Dan Schechtman experimented with a combination of aluminum and magnesium. When he cooled the alloy quickly he found that the subatomic crystal structure formed a Penrose pattern. Because the crystal formation did not repeat like a regular crystal, it was dubbed a quasicrystal. Up until that point in the study of crystals, aperiodic tilings were considered forbidden—even impossible.

Dr. Schechtman received much ridicule for his discovery, but was eventually vindicated by winning the Nobel Prize in Chemistry in 2011. In the 1990s, theoretical physicist, Dr. Paul Steinhardt, inspired by Schechtman’s discovery of quasicrystals, began looking for naturally occurring quasicrystals. He and his team examined thousands of crystal samples from all over the world. Eventually they found a quasicrystal in a rare 4.5 billion year old meteorite. As it turns out, the quasicrystal does not naturally occur on earth, it’s alien origin aligns with the creation of the galaxy. When I began working with diffracting the Penrose using digital projection in Diffract You, I considered the organic mutations that developed from what started out as a rigid system. Could there be other processes that exist in alien environments that create strange and wonderful life? Science is forever on a quest for hard evidence of its existence. As much as I would love to see that evidence that is not my goal as an artist. I consider my work a daydream of what could be—musings on the forms and shapes of structures that are far from our common perception.

In my research of quasicrystals, I came across the work of artist Tony Robbin. Recently, I had the pleasure of meeting Robbin in his studio in Manthattan. His career began in the early 1970s as one of the founding members of the Pattern and Decoration movement. The P&D movement, which embraced multiple cultures of pattern, grew out of a rejection of minimalism that had a strangle hold on art and architecture for the latter half of the twentieth century, and beyond. It was during that same period of the 1970s that Dr. Penrose was working out the tessellation of the Penrose pattern. Robbin’s interest in pattern and spatial complexity via painting and sculpture intersects my interest in quasicrystals and the perception of reality. He was kind enough to show me his beautiful paintings that at times fool the eye and mind into a perception of space that goes beyond 3 dimensions. His extensive study of 4 dimensional projective geometry, quasicrystals and computer visualizations allowed Robbin to expand his spatial capabilities. His paintings took on much more visual information after he learned how to manipulate 3D modeling software. [figure 6] Robbin created an impressive 3D quasicrystal sculpture in Denmark in 1993. Once I saw the photos on his website, I knew that it was possible to tessellate a Penrose in 3D. I had been thinking that I needed to use two shapes as I did in the 2D tessellation, but in 3D I needed four. This grouping is called the Golden Zonohedra [figure 7].

Robbin wrote several books that have been invaluable to me in my quest for understanding. I am grateful for his insights and painstaking effort to explain important scientific principals in a way that not only could I understand, but was able to put into use. Decoration and pattern in the William Morris sense references wallpaper and textiles, but in the case of mathematics, decoration has an entirely different meaning. For example, Robbin explained the technique of mathematical decoration as being directly related to inflation and deflation of pattern. The decorated tiles [figure 8] form into smaller tiles of the same shape as those used in the tiling (and thus allow bigger tiles to be made from smaller ones). This demonstrates that the Penrose tiling has a scaling self-similarity and as such can be considered a fractal. In “Decorated”, I projected the digitally decorated Penrose tiling onto four mirrored zonohedra to dramatic effect. The light bounced in multiple directions causing unexpected and beautiful striations that illuminated the walls.

The methods that I employ reference complex scientific processes, but are not necessary to understand my work. The new forms generated by ethereal, nebulous light are hybrids of terrestrial and extraterrestrial structures—possibly hinting at realities beyond our human experience. These emerging articulations are my main focus when creating my work. The distinct difference between Tony Robbin and me is that his focus rests in representing the 4th dimension directly. My interest lies in the new visual models that can be generated by creating systems of interference to aperiodic structures. In "Bragg All About It," I am exploring a technique called The Bragg Diffraction that is used to determine the substructure of a crystal. A crystal is irradiated with electrons and a pattern emerges on an X-Ray called Bragg Peaks. A very distinctive pattern [figure 9] appears when the crystal formation is aperiodic, determining that it is a quasicrystal. I projected the Bragg peak pattern through a pseudo-crystal (a mass of plastic) [figure 10]. I found that the plastic mass dulled the pattern that hit the far wall, but the opposite side of the plastic mass contained a distinctive pattern that directly corresponds to the Penrose tiling. The mass was beautifully illuminated in a way that elevated the plastic to a jewel-like crystal. These unexpected visual outcomes delight and push me forward toward my next exploration of techniques and materials.

For example, in "Forbidden," I projected the Ammann grid onto a 3D printed set of the Golden Zonohedra. The Ammann grid is a method of tessellation for the 2D Penrose pattern. The forms that are diffracted from the combination of the 3D and 2D structures are far more interesting to me than the originating substructure. The 3D forms illuminate on multiple planes, glowing like a string of lights. Calling attention to the unique geometric forms and the mirrored diffracted shapes that bounce off the wall behind it. The new form is organic and chaotic in its aesthetic appearance, yet comes from a highly ordered structure of alien origin. How many things are we unaware of that are chaotic yet come from order?

The endlessly fascinating Penrose and its multi-dimensional sibling the quasicrystal are unique in that they connect to so many aspects of our reality. Many different quasi-periodic materials have been generated in the lab. They have certain unique electrical, optical, hardness and non-stick properties. Light passes through these materials in a very uncommon way. Electrically and at different temperatures, they behave differently. When used as part of the structure of a fabric, it cannot be torn in a straight line. I find these properties exciting because I realize that there is no end to the possible uses of quasicrystaline structures, nor to the implications they will have on my work. In a small way, I am shining a light on what was only a theoretical possibility not that long ago.

Chaos theory claims that an initial set of factors sets up conditions that make it impossible to predict any future outcomes. My conclusion is that chaos has been thought of all wrong. Chaos is not just a disordered random system but a highly ordered system of repeating difference that has yet to reveal itself, giving the illusion of randomness. Each time a new form shows up, I feel a sense of connectivity to the very origins of our creation. It has been said we are all made of the stuff of stars. That notion makes me feel small in relation to the universe, but at the same time special, because my work gives me the opportunity to immerse myself in even the smallest part of the underlying structures of our very reality. ♦

© 2017 Christine Romanell. All Rights Reserved.