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Mathematician Creates Intricate Drawings Using One Continuous Line

Robert Bosch Optimization Art

Mathmetician and artist Robert Bosch combines his two disciplines in a series of intricate, maze-like drawings that he calls “optimization art.” This means that they were made with the assistance of mathematical and computer optimization techniques to accommodate certain constraints made by the artist.

In particular, Bosch is interested in making art that solves what is known as the traveling salesman problem. This optimization question entails that a salesman must visit several other locations without visiting the same place twice. The goal is to find the shortest, most efficient route that stops at every point once. Bosch solves this scenario in his art pieces using the constraint that the salesman's route must be a long, connected loop. Meaning that each of his drawings is actually one circuitous line.

“The mathematician in me is fascinated by the various roles that constraints play in optimization problems,” explains Bosch. “Sometimes they make them much harder to solve; other times, much easier. And the artist in me is fascinated by the roles that constraints play in art. All artists must deal with constraints, and many artists choose to impose constraints upon themselves.”

The complexity of Bosch's art is determined by the number of locations that he uses in the scenario. For example, the artist's depiction of van Gogh's self-portrait uses a solution for 120,000 locations, whereas the Girl with the Pearl Earring uses 200,000. When compared visually, it is clear in the darkened background of Vermeer's masterpiece that the sinuous line is more convoluted due to the higher number of locations.

Scroll down to see more examples of Bosch's art. And to learn more about it, pick up a copy of his book, Opt Art: From Mathematical Optimization to Visual Design.

Mathematician Robert Bosch creates intricate drawings using one continuous line.

Robert Bosch Optimization Art

This “optimization art” solves the traveling salesman problem.

Robert Bosch Optimization Art

This means that each image is made up of one continuous line that follows the shortest possible route without revisiting any single point.

Robert Bosch Optimization Art

Robert Bosch Optimization Art

Robert Bosch Optimization Art

Robert Bosch Optimization Art

Robert Bosch Optimization Art

Robert Bosch: Website | Twitter

My Modern Met granted permission to feature photos by Robert Bosch.

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Margherita Cole

Margherita Cole is a Contributing Writer at My Modern Met and illustrator based in Southern California. She holds a BA in Art History with a minor in Studio Art from Wofford College, and an MA in Illustration: Authorial Practice from Falmouth University in the UK. She wrote and illustrated an instructional art book about how to draw cartoons titled 'Cartooning Made Easy: Circle, Triangle, Square' that was published by Walter Foster in 2022.
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