Recursive Structures

In many fields of research that require higher-dimensional matrices, a researcher standardizes a set of bases. These are primitive vectors, and through linear combinations, these vectors reach every point within a given space. Since learning about bases in linear algebra, I've been interested in the simplest forms that serve as building blocks upon which more complex forms are constructed. For example, I would claim that truth values and logical operands serve as the bases for propositional logical puzzles, or that pixels with red, green, and blue values serve as the bases in the encoding of an image. This raises the question: what kind of bases represent life in the context of Earthworks? I'm interested in a structure that encapsulates the complexities of ecosystems, human intervention, and the passage of time.

In Shifting Grounds: Landscape in Contemporary Native American Art, Kate Morris notes that Robert Smithson, the artist who created Spiral Jetty, regarded the spiral as perhaps the fundamental shape of life. He saw it reflected in galaxies, DNA, fractals, and fingerprints. (Morris, p. 113) Artist Alan Michelson also uses spirals as a motif in his outdoor installation, Mantle; he describes the spiral shape as being inspired by the shell of the ancient, yet still-living, chambered nautilus. (Morris, p. 113) While these interpretations emphasize the spiral as a symbol of life by referencing naturally-occurring shapes, I would like to propose a shape that builds upon the well-established spiral form that was used by Smithson and Michelson–one that embodies life’s cyclical yet forward-moving nature. By extruding the spiral shape to cover a new dimension, a spring-like cylindrical form introduces the parameter of time–it represents land’s capacity for erosion, flexibility, and unpredictable expansion beyond our comprehension.

Robert Smithson’s Spiral Jetty is an earthwork that grapples with ideas of American expansionism and thus, marks the end of Manifest Destiny. Unlike monuments such as Mt. Rushmore or Crazy Horse, Smithson’s form does not conform to the language of neoclassical sculpture. (Fisher, p.130) The work’s spiral form, a shape rooted in the natural world (I think of the Fibonacci sequence), winds its way through the earth, the salt crust, and the water; it carries the message that if we continue at the rate at which we use natural resources, then perhaps, America has reached the end of Manifest Destiny. Spiral Jetty exists in the open landscape rather than within the controlled environment of an indoor gallery. As a result, it is subject to erosion. But can an earthwork engage with time more intentionally, rather than passively reacting to the effects of natural erosion?

One artist who engages with this question is Andy Goldsworthy, whose work interacts with time by using materials such as snow, water, or foliage, that evolve and decay as the temperatures and seasons fluctuate. In Watershed, Goldsworthy explores time through concentric circles. (The Trustees of Reservations) The work shifts with the four seasons, creating a continuous cycle of change — water levels rise and fall, sediment accumulates and erodes, and plant life adapts accordingly. Each season leaves a trace behind. In contrast, Goldsworthy's Snow House operates on a different measure of time, not in seasonal cycles but in the span of a year. (Moyer, p. 34) By tracking the rate of snow melting each year, one could derive a rough model to estimate the progression of environmental change. Additionally, it's worth noting that Snow House is shaped like a dome, constructed of circles stacked upon one-another. This cylindrical shape emphasizes the passage of time, as the snowball gradually melts to the shape of its vessel, creating a cylinder of water at a specific height. Snow House's empirical approach is not only a unique artistic exploration but also a start towards scientific inquiry, illustrating the impact of climate change through collecting empirical data. In both Watershed and Snow House, Goldsworthy observes nature's transformation with respect to time, first with the four seasons, then with the year, urging us to recognize and measure the rate at which environmental change is occuring.

Just as Goldsworthy uses concentric circles to trace nature’s transformation over seasons and years, Alan Sonfist employs them to represent layers of time itself. Sonfist’s Circles of Time, located in Tuscany, Italy, uses three acres of concentric rings to display gradual stages of human intervention on the landscape. (Sonfist, p. 261) Each ring traces the evolution of the land from its "untouched" forest to its present-day agricultural role. By physically moving inward through these layers, the viewer experiences time in reverse. This inward journey is recursive by nature, the outcome of the nth layer is contingent on the one preceding it, eventually revealing the land’s original state.

I'd like to think that the relationship between concentric circles and cylindrical or spring forms is quite intimate. Concentric circles, when stacked vertically, form a rotational form — transforming a two-dimensional representation of time and space into a three-dimensional volume. Similarly, stacked circles can also create a spring, introducing motion and elasticity. The feature of elasticity parallels the way time can be perceived as a continuous, evolving process that is not always experienced linearly. In Sonfist’s Circles of Time, each ring signifies a historical layer, a fixed point in the landscape’s transformation, discretizing time. In contrast, a spring-form suggests that these layers are not simply static–through compressing and releasing tension, the past engages with the present and future in a dynamic fashion. By orienting circles into a spring-like form, we can better imagine the dynamic conversation between human intervention and the landscape.

A cylindrical spring introduces time as an additional parameter. Unlike a fixed shape, the spring embodies both cyclical repetition with its sinusoidal movement. It compresses under external force, storing potential energy, and when released, that energy manifests as motion — under a controlled environment (like an art gallery), such motion is predictable, but when we introduce new variables (such as weather, erosion, human intervention in the landscape, etc.), the outcome can become chaotic. As natural resources are depleted and ecosystems are pushed beyond their limits, the land accumulates stress, much like a compressed spring. The eventual release of that stored energy — whether through ecological collapse, natural disasters, or resource scarcity — follows a trajectory that is difficult to predict, much like an oscillating system that is influenced by external forces.

Hence, I believe that a cylindrical spring is a more fitting representation of the dynamic relationship between mankind and the landscape. The spring captures the essence of tension, potential, and release. In the current trajectory of environmental change, we can see humanity’s increasing impact on the land, which is storing up energy and pressure. As those who hold positions of power continue to exhaust natural resources, pushing the boundaries of our development, consumption, and ecological transformation, humanity risks creating a moment where that spring’s potential energy is released in ways we can’t predict or control.

Morris, Kate. Shifting Grounds: Landscape in Contemporary Native American Art. Seattle: University of Washington Press, 2019.

Fisher, Joshua. “Empire Makers: Earth Art and the Struggle for a Continent.” Public Art Dialogue 1, no. 1 (March 2011): 119–136.

“Andy Goldsworthy — Watershed.” The Trustees of Reservations. Accessed February 26, 2025. https://thetrustees.org/content/andy-goldsworthy-watershed/.

Moyer, Twylene. “Andy Goldsworthy.” In The New Earthwork: Art, Action, Agency, edited by Twylene Moyer and Glenn Harper, 32–35. Seattle: University of Washington Press, 2011.

Sonfist, Alan. Nature: The End of Art — Environmental Landscapes. New York: Collins & Brown, 2004.

7/8/2025