Time-Shifting Geometries

This writing introduces concepts and methodologies behind my algorithmic plotter graphics series "Procedural Drawings" that is exhibited as part of EXPANDED.ART Gallery’s 'THE PATH TO THE PRESENT, 1954–2024' satellite exhibition, taking place on the occasion of the Generative Art Summit Berlin, 2024

Procedural properties are ancient problem solving techniques in communication, art, crafts and all type of mental activities. We can see its incarnations in everyday life from architectural ornaments through handmade indian kolam and rangoli layouts to formalised design practices, mathematics, geometry, music, and code based algorithmic systems. Controlling such processes involves a continuous cognitive effort from the maker: a presence of focus and awareness, combined with varying levels of openness and acceptance towards unintended consequences that might be caused by the pre-scripted rules.

Chinese landscape painters often say the mountain, the trees, the water and other natural elements are living, active entities within their compositions. The physical environment in combination with the abstract compositional elements are shaping a complex ecological system. Apart of the entities of the landscape, these concepts incorporate many other non-human elements including spirits, deities, intuitive heuristics, metaphysical processes and supernatural components that conclude in formations which could also be described as an example of an extended mind. In fact, from time to time artists and cultural practitioners involve their medium and the surrounding environment in various ways to represent their emotional issues, intellectual questions and multimodal complexities in accordance to societal challenges or personal aspects of existence.

These collective, environmentalist approaches have many analogies with contemporary digital culture, especially algorithmic art practice, where creating an artwork involves myriad contributors along the process: network infrastructures, electricity, distributed code libraries and other software components, operating systems, server hosts, technical protocols, visual algorithms and geometrical formulas to name but a few. Procedural or rule based image creation traditionally uses geometric patterns, deterministic systems and symbolism to convey cultural stories and beliefs in both its early appearances and in contemporary practice. Indigenous artworks made for rituals often involve community collaboration and are integral to rituals and ceremonies. Similarly, digital art projects frequently invite global participation, shared code base, sophisticated social protocols and mechanisms that turn interactive activities into communal experiences. Both preserve and innovate cultural expressions, blending traditional motifs with new media. This connection highlights their shared focus on cultural narratives and their adaptability in a digital society.

A very beautiful procedural example is the system made by Aristid Lindenmayer who was trying to describe complex biological and natural growth with a simple set of rules. This system is named after him. He also wrote a really inspiring book on “The Algorithmic Beauty of Plants”. He wanted a way to test his theory about the growth pattern of a particular type of algae. His theory stated that the cells of this algae could be in one of two states: growth or reproduction. An algae in the growth state eventually grew into the reproduction state. An algae in the reproduction state eventually divided into two cells, one of which was in the growth state and the other in the reproduction state. Lindenmayer’s grammar system proved a fantastic method for proving his theory. What Lindenmayer could not have predicted is the incredible usefulness of his system in many other areas, both in biology and in mathematics.

A Lindenmayer grammar is fully defined by an initial axiom and a set of one or more transformation rules. The initial axiom consists of a “string” of characters (e.g., alphabetic letters, punctuation, etc.). Each transformation rule gives a set of characters to search for in an axiom, and a set of characters to replace the original characters with. Applying all of the transformation rules to the initial axiom produces a new axiom. The rules can then be applied to this second axiom to produce a third axiom. Applying the rules to the third axiom produces the fourth, and so on. Each application of the transformation rules is called an iteration of the grammar. Growing line structures this way can create great complexity from a simple set of axioms. Any time you have a long flexible linear object, and a desire to have that object take up a small space, you enter into a special realm of geometrical problem-solving – a realm that involves twisting, turning, bending, folding, and wrapping. This geometric realm is also invoked for the purpose of creating convoluted paths to follow, like a maze or a labyrinth.

While the deterministic nature of an L-System describes very well some aspects of rule based creation processes, there are many other insightful approaches for operating complex relationships based on simple elements. From an artistic point of view, the computational aspects of the I-Ching also offer rich sources of inspiration. As opposed to L-Systems and pure determinism, the essence of this method is mainly based on randomness and chance operations. The I-Ching, also known as the Book of Changes, is an ancient Chinese divination text and one of the oldest classics of Chinese literature. Its structured yet dynamic system of hexagrams, the interplay of binary oppositions, and the deep symbolism embedded within its text provide a fertile ground for exploration in various ways of artistic experiments especially in the fields of algorithmic and generative art.

The I-Ching embodies the concept of change through the dynamic interplay of binary oppositions (yin and yang). Randomness is used through the casting of yarrow sticks or coins to generate hexagrams, embodying the principle of chance to determine the specific combination of yin and yang lines that form a reading. Each hexagram is not static; it represents a state of transformation, capturing a moment within a continuous process of change. Using randomness in artistic systems become interesting when one starts to adjust the different distributions and probability parameters of the system. A random sequence of events, symbols or steps often has no order and does not follow an intelligible pattern or combination. Individual random events are, by definition, unpredictable, but if there is a known probability distribution, the frequency of different outcomes over repeated events (or "trials") is predictable. Procedural Drawings consist of visual systems that incorporate determinism, randomness and computational thinking that have a structure that is built from the bottom-up: initial states and conditional parameters affect largely the outcome of the resulting image by interpreting the algorithmic instructions accordingly. The central authority of the artist takes part only at specific stages of the creation process. Such specially emphasized intervals can be located at the beginning of a process (writing the code and the instruction set) and at the end, (curating and selecting the generated outputs). The decisions and procedures in-between are distributed among all components of the autonomous system.

The images of Procedural Drawings are the outcomes of operations where a system begins to rearrange an initial field of evenly distributed, parallel lines. The resulting wrinkles, repetitions, and overlapping forms produce organic patterns on one hand, while preserving the raw, machine-like line structures of the computer on the other. The shapes are then converted into vector line segments in order to be able to trace out with a plotter machine through a contemplative procedure that might take several hours. The transformations are irreversible, moving from order towards disorder, thereby increasing the level of entropy within the system.

There is a natural shift from order to disorder, reflecting impermanence, chaos, and the passage of time. The artworks depict decay and transformation using algorithmic procedures that wear and change, that might resemble rusting metals or melting ice. Entropy also serves as a metaphor for ecological and societal issues, that might be associated with the inevitable transformation of all things.

There is a common element that takes an essential organising agency within all the drawings: empty space, or negative space (Japanese ma, 間, lit. 'gap, space, pause'). By applying a shape mask on the edges of the compositions, the lines in the foreground become entangled with the empty void of the background. Varying sizes of empty spots are reframing the overall structure of the image field, which adds a vivid and delightful visual rhythm to the composition. In modern interpretations of ma, it is often taken to refer to an artistic interpretation of the empty space, often holding as much importance as the rest of an artwork and focusing the viewer on the intention of negative space in an art piece. Though commonly used to refer to literal, visible negative space, ma may also refer to the perception of a space, gap or interval, without necessarily requiring a physical compositional element.

Procedural Drawings are made of consistent structures, where each piece is part of a larger cluster of works, with similar image architecture, same resolution and pen width, with varying constellations of color palettes: each piece is monochrome, so the quality and density of the lines are the elements that create the dramaturgy over the scenes. The series consist of three different ink and paper color variants. The grey paper with black ink resembles a more traditional graphic appearance that might recall classical etching, mechanical sketches, typewriter drawings or architectural plans. The black paper with silver ink is a bit more immersive which brings forward chalk drawings, embroidery, circuit board layouts, but also reflects on the aforementioned temporary compositional structures like kolams, rangolis, yantras and other shapes of ritual geometries. The last variation is using blue paper which color is derived from the third channel of the RGB computer screen. This is the color of in-between states in the digital bardo. You usually see blue when an operating system crashes or an imaging device has no input signal.

During my walks outside of the studio, I often think of these drawings as async in their nature. This would mean they have a special relationship with time. As opposed to regular, realtime digital media where the code you write immediately appears on the screen in sync with your intention, in the case of plotter drawings, you have to wait for the initial idea to take its final form. While evaluating the rules and unfolding the vectors that are encoded in the file using a slowly moving, contemplative machine you have time to observe the details and engage in a deeper conversation with the work itself.

This rhythmic pattern of creation also effects the curation process - there are many qualities and nuances that must be present in a work to have it selected to plot and sacrifice time, material and energy upon its making. The process of working with a slow, async apparatus can sometimes shift out from the mindset of measured time into one of unmeasured time. This often involves stepping out of time itself which can include periods of very purposeful, intuitive contemplations beyond the artwork. It is a unique mode of temporality, decoupled from the normal attachment to time, the opposite of being busy. This transition of shifting in time isn’t about moving around the blocks on your calendar — it’s about learning how to shift between different rhythms of temporality.

Procedural Drawings is currently on view at EXPANDED.ART Gallery. Special thanks to Anika Meier for the curation and for making the exhibition and the summit possible.

Anni Kumari - Significance of Kolam in Tamil Culture
Giacomo Bruni - Ecological Culture in Chinese Traditional Mountain and Water Painting
Aristrid Lindenmayer - Algorithmic Beauty of Plants
Cliff Guren - The Art of Time-Shifting
Steve Marshall - John Cage’s I Ching chance operations
Alex Estorick & Aleksandra Jovanić - The Power of the Plotter (interview)
Andy Clark - The Extended Mind