Interpolation in Computer Art, Part One: A Brief Personal Tour
This article presents a brief survey of interpolation in computer art, as the conceptual framework for a “pedagogical sketchbook” of computational artworks that interpolate from a circle to a triangle. To view the sketchbook, see Part Two of this article. To quickly browse the sketchbook NFTs, visit here.
From November 1–14, 2021, on the occasion of the 20th anniversary of the Processing initiative, the fourteen pages of this sketchbook are being released as a series of daily NFTs—20% of the proceeds from which are automatically shared with the
using a new smart contract. It is my hope that this project can help serve as an example of a new mode of charitable support for open-source arts.
This article is adapted from presentations originally given in October 2017 in a guest tutorial on the Coding Train YouTube channel, and in the Computational Design: Practices, Histories, Infrastructures symposium at the Frank-Ratchye STUDIO for Creative Inquiry, Carnegie Mellon University. If you prefer to watch a half-hour video version of this article, please see this:
A Brief Personal Tour of Interpolation
Let us consider transformation. Who cannot but wonder at the natural marvel : the mysterious metamorphosis of a caterpillar, which architects a chrysalis, in which it turns, privately and away from our eyes, into a butterfly.
Transformation is not just natural, but often, a sign of the supernatural. Jesus’s first miracle is specifically one of transmutation. In John 2, Jesus delivers such a sign at the Wedding at Cana—by turning water into wine.
For many observers, it is not enough to know that a transformation has occurred; we yearn to witness how this metamorphosis takes place, step-by-step, to understand its magic or savor its details. Perhaps we want epistemic proof of the continuity of the transforming subject’s identity. We want to observe intermediate stages—to somehow see inside the butterfly’s pupa — as suggested in this political cartoon of 1831, by Charles Philipon, which illustrates the progressive degradation of the effectiveness of the King’s rule through a series of Tuftean small multiples.
M.C. Escher’s ingenious Metamorphosis uses a different visual strategy; rather than a grid of isolated units, he attempts to show as continuous and as gradual a transformation as possible. As Escher wrote to his son: “I feel compelled to ‘add new metamorphoses, or transitional stages.’”.
Whether producing small multiples, still image sequences or animations, the computer is an ideal tool for visualizing these in-between states of form. How better could one generate the covers of “Animorphs”, a popular series of books — appropriately enough written for tweens — who are themselves grappling with wild and frustrating changes to their bodies. Here is a child who turns into a horse. Another turns into a starfish… or perhaps the reverse.
On the computer, transformations from one form to another are known by many names. CAD engineers, architects, and product designers, for example, using a term borrowed from boat-making, call it lofting.
With photographic media, the process of interpolation is called morphing—the first technology for which was developed by Nancy Burson as an artist-in-residence at MIT Center for Advanced Visual Studies in the early 1980s. Her software was ‘face aware’, and used landmarks for things like eyes and noses, in order to produce interpolated images that went far beyond simple blends or multiple exposures. In her First and Second Beauty Composites (1982), Burson used this technique to explore shifting standards of idealized female beauty, creating composite movie stars from the 1950s and 1970s. Burson’s synthetic portraits are snapshots of the in-between.
In fact, interpolation as both subject and technique has featured significantly in computer art practice since its earliest days. Influenced by cybernetic theories (Shannon, Bense) of signal and noise, some of the first artists to use a computer created transformations that examined the relationship of form to randomness, through the progressive corruption of a simple design. Here is “Chaos to Order”, a plotter artwork made in 1967 by Charles “Chuck” Csuri and James Shaffer.
Likewise, “P-112, Lady Quark” (1972) by Manfred Mohr is a collection of nine squares that uses interpolation to explore the path from structure to disorder. Each square is progressively transformed, over the course of 23 iterations, into a randomized, crinkly polygon.
Other works from this period explore the space between two forms, without the influence of randomness. In the 1967 “Return to Square” by Masao Kohmura and Kunio Yamanaka, members of Japan’s CTG (Computer Technique Group), the ideal form of a square is metamorphosed into the profile of a woman, and then returned to a square again. Several versions of this work exist, including versions with exponential and linear interpolation.
in 1967, Chuck Csuri and James Shaffer created “Aging Process (Transformation)”, a drawing rendered on a drum plotter by an IBM 7094. It is an attempt to see an evolution that happens to all of us, and everyone we know. But it does not work as one might (naively) expect, showing a person changing from young to old. The project is full of “glitches”, because the marks are not well parameterized.
The computer truly comes into its own when we ask it to show the intermediate states in otherwise impossible or unknowable transitions between forms we know well. This lovely but little-known work is “Fruit Salad” by Guus Craenen and Adrian Hane, from 1970. At the four corners are a platonic apple, lemon, orange, and a chestnut (which I guess for argument’s sake, is a fruit). But inside the square, are the uncanny mixtures.
Although bananas and ice cream cones are both foodstuffs, it is not clear how one could meaningfully parameterize their transition. William Kolomyjec stated that this attempt from the early 1970s, which depicts a linear interpolation of 99 points, allows the hybrid treat to be consumed “again and again”.
The pinnacle of puzzling interpolations may be CTG’s “Running Cola is Africa!”, a well-known computer artwork that appeared in the landmark 1968 Cybernetic Serendipity exhibition of computer-based art.
Fast-forwarding half a century, interpolation is now a core tool in contemporary artistic experimentation with generative adversarial neural networks, or GANs. Artists train highly complex models from thousands or millions of exemplar images, navigating the in-betweens of wildly high-dimensional “latent spaces” to make otherworldly discoveries like Helena Sarin’s Leaves of Manifold.
In much of my own work, I strain toward the absolute, and seek to eschew the arbitrary. A touchstone for me is Wassily Kandinsky’s 1926 manifesto of modernist form, Point and Line to Plane. Kandinsky defines the triangle and the circle as the “primary contrasting pair” of planar forms—the maximally and minimally pointy, if you will.
To me, there is something deep about such absolute forms: they are eternal talismans that own the purity of mathematics. And yet: amidst all the bewildering complexity of the real world, it should not surprise us at all how confounding, and even how human, our relation to such simple forms can be.
As the circle and triangle are logical extremes of a sort, there is naturally a history of creating a gradation between them. The hand-drawn examples shown here are from Wucius Wong’s 1972 introductory text, Principles of Two-Dimensional Design. I especially admire the cleverness of his bottom row. It is the silhouette of a cone, rotating from a plan to section view.
As you can imagine, there are many ways of getting from a circle to a triangle. In Part Two of this article, I would like to share with you some of my own attempts. During winter break 2017, I allowed myself one week to design every possible animated transformation between a circle and a triangle that I could think of. I devised fourteen methods, and implemented them in p5.js, a free JavaScript software toolkit for the arts.
Part Two of this article, a New Pedagogical Sketchbook, presents the full set of these fourteen interpolations, formatted as animated GIFs, and published daily from November 1–14, 2021, as low-carbon NFTs on the Tezos blockchain. An example of one such interpolation is shown below.
References
- Nancy Burson, “First and Second Beauty Composites”, 1982.
- Joseph Choma, “Morphing: A Guide to Mathematical Transformations for Architects and Designers”, 2015.
- Guus Craenen and Adrian Hane, “Fruit Salad”, 1970, in “Computer Graphics, Computer Art”, by Herbert W. Franke, 1971.
- Chuck Csuri and James Shaffer, “Chaos to Order” and
“Aging Process (Transformation)”, 1967. - CTG Japan (Masao Kohmura, Koji Fujino, Makoto Ohtake, Kunio Yamanaka), “Running Cola is Africa!” and “Return to Square”, 1967-1968.
- M.C. Escher, “Metamorphosis III”, 1967–1968.
- Wassily Kandinsky, “Point and Line to Plane”, 1926.
- Paul Klee, “Pedagogical Sketchbook”, 1925.
- William Kolomyjec, “Banana Cone”, 1970–1975.
- Jürg Lehni and Wilm Thoben, “Footnotes from the History of Two Cultures: Mitsuo Katsui”, 2015.
- Manfred Mohr, “P-112 / Lady Quark”, 1972.
- Bruno Munari, “Square Circle Triangle”, 1960–1976.
- Charles Philipon, “Les Poires”, 1831.
- Jason Salavon, “Still Life (Vanitas)”, 2009.
- Helena Sarin, “Leaves of Manifold, of Red and Gold”, 2019–2021.
- Dan Shiffman, “10 Minute Coding Challenges — Shape Morphing”, 2016.
- Dan Shiffman, “Coding Challenge #19: Superellipse”, 2016.
- Troika, “Squaring the Circle”; “Dark Matter”, 2013–2014.
- Wucius Wong, “Principles of Two-Dimensional Design”, 1972.
- Yuki Yoshida, “A Book of drawCircle()”, 2014.
Acknowledgments
I am grateful to Dan Shiffman, the Coding Train, and Daniel Cardoso-Llach for hosting the talks that led to this publication; to
, , , and the for creating toolkits that have given livelihoods to myself and so many others; and to @1x1_NFT for the privilege of using a beta test of the new collab contract.