What Plus What Equals 17
Products of a arrangement are generally expected to accept a sure rigidity. A system is ostensibly a rational enterprise, meant to achieve its objective with greater efficiency than the improvisations of an unsteady homo mitt. And with that absence of improvisation comes an absence of graphic symbol and warmth. After all, though the system may take been created by humans, its products are at least one step removed from that humanity: Les Paul's signature may be on your guitar, but Les Paul himself almost certainly never touched it, and he may never have fifty-fifty entered the manufacturing plant that produced it.
My Plus Equals explorations then far accept mostly embraced the rigidity their combinatorial systems produce (Fig. one). Like their forebears in the conceptual and minimalist art movements, they're a counterpoint to the gestural immediacy of something like abstract expressionism, and their mechanical lines and comprehensive seriality establish their own kind of regulated dazzler. That said, the systems I devise don't accept a mandate to make stiff work, and the prospect of finding something alike to gestural immediacy within a rigid structure is a contradiction that interests me. And 1 fundamental way to explore that contradiction is to expect at the human relationship between straight lines and curves.
While working for the automaker Citroën in 1959, the French physicist and mathematician Paul de Casteljau developed a method for computationally describing and creating curved lines. A short fourth dimension later, an engineer named Pierre Bézier independently made the same discovery and applied information technology to the pattern of automobile bodies at Renault, another French auto company. Different de Casteljau, Bézier didn't hesitate to publish his findings, and so the method, which is notwithstanding widely used today in the design of everything from fonts to video games to the aforementioned Les Paul guitars, became known every bit the Bézier curve.
Bézier curves come in a few dissimilar flavors, and the one best suited to my purpose is the cubic Bézier curve. Information technology's divers by four points on a plane: 2 cease points—let's call them A and D—and 2 command points, B and C (Fig. 2). The positions of the end points make up one's mind the beginning and end of the bend, and through a process of linear interpolation, their spatial relationships with the positions of the command points determine the shape of the curve itself. To see how it works, first draw straight lines betwixt A and B, B and C, and C and D (Fig. iii). Next, marker the midpoint on each of those lines and describe lines connecting the AB midpoint to the BC midpoint, and the BC midpoint to the CD midpoint (Fig. 4). Finally, mark the midpoints of those lines and draw i final line connecting those midpoints. The midpoint of that final line, which we'll telephone call P, is the midpoint of the curve (Fig. 5). If we proceed the original four points in the same positions, but redraw the rest of the apparatus, this time placing the interior points 25% of the way across the connecting lines, P now marks the 25% signal on that same bend (Fig. six). Redraw the apparatus plenty times, moving the interior points incrementally each time, and P will eventually shape the entire bend between A and D. (Fig. vii).
A chain of curves produced in this manner can form whatsoever shape imaginable (Fig. 8), and to do so by applying a relatively simple algorithm to a limited number of signal coordinates is incredibly powerful, so it's not hard to see why the discoveries of de Casteljau and Bézier have been so influential. (For a deeper swoop into Bézier curves, I highly recommend Bartosz Ciechanowski's interactive explainer, "Curves and Surfaces," and/or Freya Holmér's video, "The Beauty of Bézier Curves.")
Bézier curves have the potential to give me what I'1000 looking for: Their end points and control points can exist plotted according to a strict system, and the resulting curves can yet evoke the looseness of human gesture.
The foundation of my strict system is a 3×iii grid. The first office of the programme is to find every possible sequence of points within that grid, where 1) each sequence starts at the aforementioned indicate, 2) each point is a distance of one×two or 2×1 grid units away from the indicate preceding it, and 3) no point is used more than once in a sequence. Each sequence volition plot the finish points for a concatenation of Bézier curves.
I begin past choosing bespeak 2,2 every bit a somewhat central origin point for all sequences. At that place are four points in the grid that are the specified distance from that point: 0,ane, 0,three, i,0, and iii,0 (Fig. nine). These make the beginnings of four sequences, and each of them is able to branch out to one or more additional points (Fig. 10). Any fourth dimension a sequence has more than 1 candidate for its adjacent signal, a new sequence is formed for each additional candidate (Fig. eleven). A sequence is complete when information technology reaches a dead end (Fig. 12). This procedure ultimately produces 562 distinct sequences, with lengths ranging from four to 14 points.
Now for the control points, which volition be positioned on the same filigree. Using the same point names from our earlier Bézier curve demo, I'll place each B control bespeak one filigree unit away from its corresponding A end point, and likewise, I'll place each C control betoken i grid unit of measurement away from its corresponding D end signal. To give the curves some multifariousness, the control points tin be positioned horizontally, vertically, or diagonally, relative to their corresponding end points (Fig. thirteen).
The control points could only cycle through those directions: the offset end point in the sequence gets a horizontal control indicate, the 2nd is vertical, the third is diagonal, the fourth is horizontal, the fifth is vertical, and then on. Even so, many of the finish point sequences are identical to each other apart from their final few points, and having every sequence use ane directional cycle for their command points would make most of their curves identical too. If I'm going for an effect of spontaneous gesture, that kind of repetition won't assistance (Fig. fourteen).
So I made a ready of six different directional cycles (Fig. 15). The first cease point sequence'due south control points use the first directional bike, the second sequence uses the second cycle, and and then on. This allows similar sequences of end points to produce very different curves (Fig. 16).
With repetition obscured and diverseness achieved, the final production is a serial of 562 scribbles that you might not have guessed were all drawn by an algorithm (Fig. 17).
I of the start things I noticed nearly this series is that despite the uniqueness of its private scribbles, they all seem to have a consistent personality. Throughout the series, the system generates some loose motifs, which imbue the scribbles with a shared character, every bit if they collectively stand for one person'southward handwriting in the absence of an alphabet. And that person seems to be expressing something, albeit in a subtly regimented manner. Information technology's not hard to see in these scribbles anger, joy, confusion, or even colorlessness, and yet these emotional qualities never manage to empower the scribbles to escape their confinement. They all occupy their uniform allotted space with robotic obedience.
Every bit much as I'm enjoying the discoveries that come with venturing into seemingly spontaneous and organic combinatorial forms, I'm ambivalent about the achievement.
Bogus intelligence has made real strides this year, most noticeably in the grade of machine learning models that generate digital images from natural language descriptions. These models have been trained to associate images with relevant words by studying hundreds of millions of captioned pictures. When given a descriptive prompt, like, say, "Photo of an astronaut playing the piano, in the style of Dorothea Lange," they can generate photorealistic images in mere seconds that return that scene with startling accuracy (Fig. 18). As a landmark technological advancement, it's in line with what we've come to look from Silicon Valley, in that it's both astonishing and unnerving, shaped past deep pockets and fanciful libertarian ideals, and there'southward no shortage of reasons to be skeptical that nosotros're set up for its implications.
The trajectory of the cyberspace over the last 30 years—from its techno-utopian colonization in the 1990s, to its capitalist co-option in the 2000s, to its obliteration of the very notion of objective truth in the 2010s—has fabricated Luddites out of many of us who were in one case optimistic most its promise. It's hard to square the undeniably positive furnishings of computers' growing ubiquity with their power to enable harm at a previously unimaginable scale. AI has the potential to cure disease, feed the world, and amplify our imaginations. Simply can it avoid embodying our worst biases and existence weaponized for targeted abuse, the spread of disinformation, and who knows what else? Tin can information technology re-found our social rubber internet with the same speed it displaces workers? Can it reshape our ideas around authorship and ownership?
The series of scribbles I've generated hither is obviously nowhere most the level of sophistication of artificial intelligence. Merely it does live somewhere in the uneasy realm of computers pretending to exist human. We'll all exist living in that realm eventually. Hither'southward hoping that against the odds, it'south a harmonious one.
Rob Weychert
rob@robweychert.com
What Plus What Equals 17,
Source: https://plusequals.art/06/
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