Maps of the World in Its Becoming: Visual Essay
From a recent group show I was in:
“Once there were brook trout in the streams in the mountains. You could see them standing in the amber current where the white edges of their fins wimpled softly in the flow. They smelled of moss in your hand. Polished and muscular and torsional. On their backs were vermiculate patterns that were maps of the world in its becoming. Maps and mazes. Of a thing which could not be put back. Not be made right again. In the deep glens where they lived all things were older than man and they hummed of mystery.” — The Road by Cormac McCarthy
Artist Statement
I began experimenting with Turing patterns in my neural network practice as a sort of joke. Reaction-diffusion systems are a common tool in generative art, and I found the idea of recreating these generative patterns using a generative neural network as funny in a formalist pun sort of way.
Adding to the formalist pun is the fact that both neural networks and turing patterns utilize diffusion. Gradient diffusion is a key technique used in backpropagation, the training of neural network models, and diffusion is the process by which Turing patterns operate. Turing patterns and gradient diffusion are related only in the broad sense that they both involve the propagation or diffusion of information, but the specific mechanisms and mathematical frameworks are quite different (or so I’m told, I’m bad at math).
Turing patterns form the basis of many patterns we see in nature, such as brain coral, the patterns of a leopard’s coat, the molars of a mouse, and yes the vermiculite pattern of a trout’s camouflage.
This quote from Cormac McCarthy’s The Road has stuck in my head for years. The Narrator muses on the mystery and wonder of the deterministic world. The world is like an impossibly complex reaction-diffusion system, and we are around for a very short slice of its evolution.
Miscellaneous Explanations
What is a reaction diffusion system and Turing pattern?
A reaction diffusion system is a mathematical model that describes how the concentrations of one or more chemical substances change over space and time due to both reaction and diffusion. Turing patterns are the resulting patterns from these systems.
The core concept of a reaction-diffusion system is straightforward: it involves two chemicals, one serving as an activator and the other as an inhibitor. The interplay between these activator and inhibitor chemicals gives rise to what is known as the Turing pattern. Unlike a top-down approach seen in human urban planning, where a higher authority dictates the layout of roads, reaction-diffusion systems are decentralized. They generate patterns through the bottom-up interaction of the system, without external guidance. To illustrate, consider the difference between a carefully choreographed musical number and the spontaneous, decentralized dynamics of a dance party.
“The Turing pattern is a concept introduced by English mathematician Alan Turing in a 1952 paper titled “The Chemical Basis of Morphogenesis” which describes how patterns in nature, such as stripes and spots, can arise naturally and autonomously from a homogeneous, uniform state. The pattern arises due to Turing instability which in turn arises due to the interplay between differential diffusion (i.e., different values of diffusion coefficients) of chemical species and chemical reaction. The instability mechanism is unforeseen because a pure diffusion process would be anticipated to have a stabilizing influence on the system.
In his paper, Turing examined the behaviour of a system in which two diffusible substances interact with each other, and found that such a system is able to generate a spatially periodic pattern even from a random or almost uniform initial condition. Prior to the discovery of this instability mechanism arising due to unequal diffusion coefficients of the two substances, diffusional effects were always presumed to have stabilizing influences on the system.
Turing hypothesized that the resulting wavelike patterns are the chemical basis of morphogenesis. Turing patterning is often found in combination with other patterns: vertebrate limb development is one of the many phenotypes exhibiting Turing patterning overlapped with a complementary pattern” — — https://en.wikipedia.org/wiki/Turing_pattern
What is art formalism?
Art formalism is used to refer to an approach to analyzing or creating art, which primarily focuses on the “form” of the art. IE: it’s color, shape, composition, size, texture, material, etc
To me, art formalism means thinking about how the material limits of the medium inform its final output. Oil paint acts one way, watercolor another. Ithink most “innovation” in art comes from people testing the limits of new mediums and figuring the boundaries of how things work.
Renoir is quoted: “Without paint in tubes there would have been… nothing of what the journalists were later to call Impressionists.” Pre-mixed colors allowed for more diverse colors, and made paint portable, allowing for painting en plein aire (Outside of the studio in direct observation of the natural world.).
When I say “formalist pun” in my artist statement, I mean that I’m playing around with the limits of the medium. I’m subverting the normal use case for a medium by bending it to fit something else.
In more traditional generative art a reaction diffusion system is directly simulated.
Here’s a fun interactive model of a reaction diffusion system:
https://rreusser.github.io/multiscale-turing-patterns
You can find a notebook with code you can explore here: https://observablehq.com/@rreusser/multiscale-turing-patterns-in-webgl
This one is also cool and gives a better visual of a reaction diffusion system over time: https://observablehq.com/@mbostock/gray-scott-reaction-diffusion
In “Maps of the World in Its Becoming”, the reaction diffusion system is not simulated. Instead the Turing pattern is generated by a neural network which has been trained on images tagged based on their content. The prompt fed into Midjourney v5 was “Rainbow trout skin pattern seamless”. The neural network model is just making an image based on what it thinks fits that prompt, not actually simulating the underlying chemical process by which the pattern is formed in nature.
One thing I like about “Maps of the World in Its Becoming” is how it helped me understand the Cormac McCarthy quote anew. I’d always liked that bit for its emotive quality but only after playing with trout patterns did I get the intended theme of fatalism/determinism in it. Formalist approaches generally eschew “content”, storytelling, or conceptual meaning, but I think it’s interesting to leverage formal qualities to fill out the a piece’s conceptual intention.
Related Images
Handful of example outputs for “Rainbow trout skin pattern seamless” :
More playing around with the trout theme:
Vermiculite means “full of worms” in Latin by the way.
Disclaimer: Parts of the above text have been written in conjunction with ChatGPT and human readers, as writing partners.
