Statement
An exploration of calibration: how the visual expression and architecture of natural forms are underpinned by coded rules yet changeable with changing conditions. This line of enquiry is rooted in the intersection of mathematics and aesthetics. A mimicry of the geometric beauty of plants in particular is being constructed, deconstructed, and reconstructed. It is a consideration of mathematical truths, whose rules are rigid but whose inputs and outputs can flex. Plants and programs have underlying hard-coded digital rules (in genetic code and computer code) but changing environmental inputs can radically change visual outputs. This opens some interesting questions (subject to ongoing experimentation), such just what exactly “randomness” is.
Bibliography
- Auerbach, T. (2019-2021) Ligature Drawings (ink on paper). Available at: https://taubaauerbach.com/works.php
These drawings are analogous to my own Turtle ‘drawings’ in that they have some roots in the mathematical and linguistic, yet Auerbach’s drawings seem freer and more fluid. Perhaps due to the silky quality of ink and the liquidity of motion with which they are drawn. They capture pattern repetitions in a playful way, and the calligraphic quality intrigues me in its potential application for Lindenmayer systems: what if they were to be drawn out in ink – would they seem more playful? What if the medium with which they were visually conveyed was more calligraphic – would this betray more of their essence as rooted in formal language theory? There is a challenge with this, however, as each line in a Lindenmayer system is necessarily replaced with each iteration, it is not merely added to, as in the the way Auerbach’s drawings are a pattern which is repeatedly suffixed to the existing line of pattern.
- Enquist, B., J. (2023) ‘Tree Theory, Biogeography and Branching’, in K. Holten (ed.) The Language of Trees. Portland, Oregon: Tin House, p29-31.
Enquist opens, “Everyone knows more or less what a tree looks like”. He goes on to elucidate how the visual diversity of branching architecture is derived from common rules (much akin to what I have been experimenting with in my use of Lindenmayer systems). I have been flexing “what a tree looks like” by playing with its branching dimensions, exploring the point at which they stop looking like trees and begin to look like some other geometric structure. Enquist’s piece has helped push my enquiry by reminder of how trees interact with one another: they often grow collectively into forests and not only solitarily. The “fractal-like filling of the forest space” is a budding interest, alongside curiosity about crown shyness and the ‘wood wide web’.
- Knowles, T. (2007) Tree Drawings. Available at: https://www.cabinetmagazine.org/issues/28/knowles.php
Plants are subject to environmental variables like sunshine and rain and wind, and in some ways, themselves are computational, with coded chemistry and pre-designed processes. They don’t think ‘let me sway in the wind’, they just sway and are subject to the elements. Yet they are alive. Knowles’ tree drawings are interesting as rather than mimicking a plant using line drawing, they use the plant to make a line drawing. The sculptural characteristics of different plant species are intriguing, and the artist likens them to ‘signatures’. They are all trees, yet they are individuals as well. This highlights perhaps a limitation in my coded systems in terms of their capacity to represent reality: they are more ‘fixed’ and determined than a real plant or tree.
- Ording, P. (A Few of) 99 Variations on a Proof, 2019.
As Ording explores expressions of visual styles “by approaching the solution of a single equation in nearly a hundred different ways”, so I am investigating the aesthetic potential of set mathematical rules with different inputs and variables. Both of us are grasping at something of the beauty of mathematics, and inquiring about the “expressive, cognitive, and imaginative possibilities” that there might be. Mathematics not only faithfully applies to the real world as a way of describing it, but its logical consistency can also be used reliably as the mode of creating something visually novel. This opens questions about what newness is – are these visual expressions really something new? Or are they truths that are being discovered, like seeds that were always there, hidden in the earth, but emerge as great flowering plants when the conditions are right? Is this an investigation of creating truth or uncovering truth?
- Prusinkiewicz, P. and Lindenmayer, A. (2004) The Algorithmic Beauty of Plants. New York: Springer Verlag.
As well as being the basis for my ‘iteration zero’ and providing the theory and knowledge to understand Lindenmayer systems, this book provides other useful branches of thought which feed into my project. One such idea is that “a departure from realism may offer a fresh view of known structures”. There is something of that in my altering of the inputs of the system to change the visual output. This also leads to questions about geometry and aesthetics: when is a structure beautiful and when is it unsettling? Is the “algorithmic beauty” still “beauty” when altered to generate structures which look less natural?
Lindenmayer systems themselves are rooted in the study of formal languages and there are implications pertaining to this and the graphic communication of my project. If the visual outputs of a system are underpinned by language, is there something else being communicated here, even if the ‘reader’, looking at the graphic, doesn’t realise it? If the alphabetical and notational information underneath the system is “F[+X][-X]FX”, is a reader necessarily reading “F[+X][-X]FX” by looking at the graphic?
- Tenen, D. ‘Literature down to a pixel’ Plain Text: The Poetics of Computation, Stanford: Stanford University Press 2017 pp. 165-195.
Tenan’s description of the illusion of digital textuality is interesting: there is a fundamental dynamic property to anything projected onto a screen, even if it seems to be a static image. In a similar way, plants minute-by-minute might seem static in their growth, despite their growth being a continuous process. This is interesting to think about because there is a sense in which plants’ development might ‘jump’, as in my code between each iteration there is a ‘jump’. Plants that one day were not in bloom, bloom the next, or which one day were full of buds are the next day full of leaf.
Furthermore, Tenan’s exploration of modalities of information and physical channels of transmission parallels a budding interest I have in exploring the same rules in different media, and what these changes of media do to the textuality and perception of the mathematical truths. There may be ways in which the idea of continuousness and discreteness, the digital versus the analogue, can be demonstrated and investigated differently.