MATHEMATICS, MADE VISIBLE
A portrait,
without lifting the pen.
One line becomes a face. Five more become a world.
A famous routing problem, made visible.
Two code-based artworks created by Opus 5.5.
01 / ONE CONTINUOUS LINE
The Weaver
An imagined face emerges from one winding line. What looks like shading is the route folding back on itself.
02 / FIVE LINES, FIVE DEPTHS
The Voyager
An astronaut separates into space, suit, face, helmet, and visor. Five lines, not one. Each layer follows its own route.
A ROUTE BECOMES A DRAWING
What is the traveling
salesman problem?
Imagine a traveler with a list of cities. They must visit each city once and return to the starting point. Which order makes the whole trip shortest? That is the traveling salesman problem, usually shortened to TSP.
Choosing the nearest next city sounds reasonable. But a convenient step now can leave an expensive detour later. The challenge is the complete route, not any single move. The problem, explained by the University of Waterloo ↗
Now replace the cities with dots in a picture. Put more dots where you want darkness and fewer where you want light. Connect them in a carefully chosen order. From close up, you see a wandering line. Step back, and a face appears.
The route is the mark.
The density is the shade.
This is an established form of mathematical art, not a new algorithm invented by an AI. Work by Robert Bosch and Adrianne Herman, followed by Craig Kaplan and Bosch's TSP Art paper, explores how the placement of points shapes continuous-line images.
How the line finds its way.
The supplied code starts with an imagined subject built from mathematical shapes, lighting, and drawn details. It turns those tones into points, then works on their order.
- 01
Place the points.
A method called weighted Voronoi stippling distributes points according to darkness. Crowded regions become rich with ink; highlights stay open.
- 02
Make a first route.
A nearest-neighbor rule connects each point to a nearby unvisited point. It gives the optimizer somewhere to start.
- 03
Improve the connections.
A technique called 2-opt replaces two connections and reverses the section between them when that shortens the route. The code also includes crossing cleanup.
- 04
Open the loop. Draw.
The longest connection is removed to make an open path. The renderer smooths the path into curves and reveals it over time.
The second piece changes
the question.
The Weaver asks how much an unbroken line can describe. The Voyager asks what happens when several such drawings occupy different depths.
From the front, the sheets align into one image. As the view turns, they separate. The face is no longer just a pattern on paper; it becomes one component in a small spatial arrangement. This is a layered illusion, not a fully modeled, solid astronaut.
The recordings report 60,000 points for The Weaver and 150,000 points across five layers for The Voyager, matching the targets in the supplied code. Each Voyager layer is routed separately, so there is no single shortest-tour claim for the whole scene.
What makes this an
interesting use of AI?
Not that AI invented TSP art. It didn't. The interesting part is bringing several existing ideas together: procedural drawing, light and shadow, point placement, route improvement, and animation.
A mathematical rule becomes something you can see, pause, and think with. The code is a medium for making an idea tangible, not just an answer to a coding exercise.
If that way of working appeals to you, Get Amplified explores practical ways to build, research, and experiment with AI. It is a broader collection of lessons and worked examples, not a promised tutorial for these particular portraits.
For a regular place to explore current tools and bring questions, there is the live Sunday 1000x Lab. And if you are deciding how AI fits a project or a larger strategy, we can work through that privately.
Credits, source notes, and what you are watching
The artworks and their original code were created by Opus 5.5, as credited by the creator. This field note adds an explanation and a web presentation of the supplied screen recordings.
The recordings are silent. Editor panels have been cropped away, and the videos have been compressed for the web. Their original playback speed and full recorded duration are retained. They show the drawing being revealed, not a live demonstration of finding or proving an optimal route.
The algorithm explanation was checked against one_line.html and layered.html in the supplied project on September 23, 2026. Point counts are reported by the recordings and supported by the source settings, not independently audited from the rendered curves. Both subjects are imaginary according to the source descriptions.
Background reading: Waterloo's TSP definition; Kaplan and Bosch, TSP Art (2005); TSP solution and verification methods. These are foundational references, not claims of new research.
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