Art
The Mathematics of Opt Art – Scientific American
It’s no secret that constraints can help artists unlock their creativity. The Oulipo literary movement embraces constraints like writing a novel without the letter e; painter Piet Mondrian created iconic works of art using only primary colors within rectilinear black and white grids; 12-tone serialism in music, in which composers set strict rules for themselves about which notes can occur in which order in their work. In all of these endeavors, constraints helped artists find creative solutions to their artistic puzzles. In his recent book Opt Art, Robert Bosch describes the constraints he applies to the art he creates and the computational and mathematical tools with which he satisfies those constraints.
Each chapter introduces an optimization problem—e.g. approximating images using particular tiles—and an accessible explanation of how to translate the problem into the language of mathematics and solve it using computational tools.
Many of the examples in the book are mosaics made using different types of tiles. French priest and mathematician Sébastien Truchet appears in a portrait using modified Truchet tiles, and Barack Obama is made of 44 complete sets of double-9 dominoes. (As those examples indicate, his work is frequently playful.)
Other pieces use the traveling salesman problem instances or knight’s tours to create line art. The traveling salesman problem is to find the shortest path between a given number of points or cities, and a knight’s tour is a path on a chessboard that visits every square exactly once using moves knights can make in chess. (I wrote about Bosch’s TSP art in 2015. It was my introduction to his work, and I’ve been a fan ever since.)
For many image types, the basic idea is to pixelate the image using a grid of the desired resolution and approximate each pixel with the type of tile you’re using. This technique makes the problems discrete, so, the tools to solve them come from the field of linear optimization. From a finite number of possible arrangements of tiles or lines connecting a group of points, can we find one that minimizes or maximizes particular quantities we have chosen?
While it’s fun to learn about the math and programming tools, I thought the most valuable thing about the book was the way Bosch gives us a peek into the more subjective side of his work: how he chooses what constraints to use with what media, and the different results that can happen when he makes different choices.
Opt Art is a fairly quick read, in part because it is so chock full of illustrations and in part because the mathematical techniques Bosch uses are at their core fairly simple. In some ways, the book is a tribute to the way the same few ideas from linear algebra can be applied to different problems to get a wide array of different results. (To be clear, this is not intended to trivialize Bosch’s work at all; I think there are an awful lot of important research projects that boil down to using the same few ideas from linear algebra to solve problems in different domains in engineering, math, and science!)
Opt Art could be a good resource for an introductory course in linear optimization or for inspiration in a project-based linear algebra class. The writing is inviting, and Bosch gives motivated students and other readers the tools they will need to jump right in and start creating their own mosaics or other images using his ideas.
For those following along with my Math Reading Challenge, try this book for prompts 4 or 9. Very precocious babies can use it for prompt 2.
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Ukrainian sells art in Essex while stuck in a warzone BBC.com
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The Courtauld Gallery at Somerset House has reopened its doors to the public after a fire swept through the historic building in central London. While the gallery has resumed operations, the rest of the iconic site remains closed “until further notice.”
On Saturday, approximately 125 firefighters were called to the scene to battle the blaze, which sent smoke billowing across the city. Fortunately, the fire occurred in a part of the building not housing valuable artworks, and no injuries were reported. Authorities are still investigating the cause of the fire.
Despite the disruption, art lovers queued outside the gallery before it reopened at 10:00 BST on Sunday. One visitor expressed his relief, saying, “I was sad to see the fire, but I’m relieved the art is safe.”
The Clark family, visiting London from Washington state, USA, had a unique perspective on the incident. While sightseeing on the London Eye, they watched as firefighters tackled the flames. Paul Clark, accompanied by his wife Jiorgia and their four children, shared their concern for the safety of the artwork inside Somerset House. “It was sad to see,” Mr. Clark told the BBC. As a fan of Vincent Van Gogh, he was particularly relieved to learn that the painter’s famous Self-Portrait with Bandaged Ear had not been affected by the fire.
Blaze in the West Wing
The fire broke out around midday on Saturday in the west wing of Somerset House, a section of the building primarily used for offices and storage. Jonathan Reekie, director of Somerset House Trust, assured the public that “no valuable artefacts or artworks” were located in that part of the building. By Sunday, fire engines were still stationed outside as investigations into the fire’s origin continued.
About Somerset House
Located on the Strand in central London, Somerset House is a prominent arts venue with a rich history dating back to the Georgian era. Built on the site of a former Tudor palace, the complex is known for its iconic courtyard and is home to the Courtauld Gallery. The gallery houses a prestigious collection from the Samuel Courtauld Trust, showcasing masterpieces from the Middle Ages to the 20th century. Among the notable works are pieces by impressionist legends such as Edouard Manet, Claude Monet, Paul Cézanne, and Vincent Van Gogh.
Somerset House regularly hosts cultural exhibitions and public events, including its popular winter ice skating sessions in the courtyard. However, for now, the venue remains partially closed as authorities ensure the safety of the site following the fire.
Art lovers and the Somerset House community can take solace in knowing that the invaluable collection remains unharmed, and the Courtauld Gallery continues to welcome visitors, offering a reprieve amid the disruption.
Sudbury’s annual art and music festival is marking a significant milestone this year, celebrating its long-standing impact on the local cultural scene. The festival, which has grown from a small community event to a major celebration of creativity, brings together artists, musicians, and visitors from across the region for a weekend of vibrant performances and exhibitions.
The event features a diverse range of activities, from live music performances to art installations, workshops, and interactive exhibits that highlight both emerging and established talent. This year’s milestone celebration will also honor the festival’s history by showcasing some of the artists and performers who have contributed to its success over the years.
Organizers are excited to see how the festival has evolved, becoming a cornerstone of Sudbury’s cultural landscape. “This festival is a celebration of creativity, community, and the incredible talent we have here in Sudbury,” said one of the event’s coordinators. “It’s amazing to see how it has grown and the impact it continues to have on the arts community.”
With this year’s milestone celebration, the festival promises to be bigger and better than ever, with a full lineup of exciting events, workshops, and performances that will inspire and engage attendees of all ages.
The festival’s milestone is not just a reflection of its past success but a celebration of the continued vibrancy of Sudbury’s arts scene.
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