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Opt Art: From Mathematical Optimization to Visual Design
A fun and stunningly illustrated introduction to the art of linear optimization
Linear optimization is a powerful modeling method for discovering the best solution to a problem among a set of available alternatives. It is one of today’s most important branches of mathematics and computer science―and also a surprisingly rich medium for creating breathtaking works of art. Opt Art takes readers on an entertaining tour of linear optimization and its applications, showing along the way how it can be used to design visual art.
Robert Bosch provides a lively and accessible introduction to the geometric, algebraic, and algorithmic foundations of optimization. He presents classical applications, such as the legendary Traveling Salesman Problem, and shows how to adapt them to make optimization art―opt art. Each chapter in this marvelously illustrated book begins with a problem or puzzle and demonstrates how the solution can be derived using a host of artistic methods and media, including 3D printing, laser cutting, and computer-controlled machining. Bosch focuses on mathematical modeling throughout―converting a problem into a workable mathematical form, solving it using optimization techniques, and examining the results, which can take the form of mosaics, line drawings, and even sculpture. All you need is some high-school algebra, geometry, and calculus to follow along.
Featuring more than a hundred illustrations and photos of Bosch’s own art, Opt Art demonstrates how mathematics and computing can be used to create beauty and express emotion through amazing works of art.
Linear optimization is a powerful modeling method for discovering the best solution to a problem among a set of available alternatives. It is one of today’s most important branches of mathematics and computer science―and also a surprisingly rich medium for creating breathtaking works of art. Opt Art takes readers on an entertaining tour of linear optimization and its applications, showing along the way how it can be used to design visual art.
Robert Bosch provides a lively and accessible introduction to the geometric, algebraic, and algorithmic foundations of optimization. He presents classical applications, such as the legendary Traveling Salesman Problem, and shows how to adapt them to make optimization art―opt art. Each chapter in this marvelously illustrated book begins with a problem or puzzle and demonstrates how the solution can be derived using a host of artistic methods and media, including 3D printing, laser cutting, and computer-controlled machining. Bosch focuses on mathematical modeling throughout―converting a problem into a workable mathematical form, solving it using optimization techniques, and examining the results, which can take the form of mosaics, line drawings, and even sculpture. All you need is some high-school algebra, geometry, and calculus to follow along.
Featuring more than a hundred illustrations and photos of Bosch’s own art, Opt Art demonstrates how mathematics and computing can be used to create beauty and express emotion through amazing works of art.
200 pages, Hardcover
Published November 12, 2019
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140 people want to read
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Displaying 1 - 7 of 7 reviews
May 7, 2020
I liked this! It’s a sort of readable maths/art recipe book, full of “here are some interesting pictures and the constraint problems I solved to produce them”, with plenty of explanation of what’s going on and some of the history of the forms used.
August 10, 2020
The equations: elegant. The art: inspiring. Makes me miss Bob's math art class. :'-)
February 22, 2021
A fun easy read exploring mathematical recipes for various kinds of art. In general, well-written, and some of the art is beautiful. As is, 3.75 stars; it would've been 5-stars if Bosch had used open-source software (instead of Gurobi) and shared his programs.
May 22, 2022
What a fun read! I discovered Opt Art while reading online about the application of operations research in art. As a mathematician with a PhD in Operations Research, Dr. Robert Bosch does an excellent job presenting simple and complex OR problems and the linear contraints applied to solve for the desired image. Opt Art has a narrative/story-like feel at times; chapter 9, "Labyrinth Design with Tiling and Pattern Matching" was among my favorite because of the connection between the optimization problems being considered and the mythological story of the Minotaur.
If not a love, at least an appreciation for mathematics is, I think, important to take the most out of Opt Art. The mathematics isn't difficult, but the variables can be a lot to keep track of if you're not used to dealing with them. That said, Dr. Bosch's explanations are written with simple, accessible terms that make the barrier less imposing for the less mathematically-inclined.
The most difficult chapter for me to follow was the sixth, "From the TSP to Continuous Line Drawings," especially once I reached the branch-and-cut section. However, the TSP art pieces were also among my favorites! I was inspired at many points to shut the book and try some of these visual design problems myself. I'd definitely recommend Opt Art to my more math-favorable friends.
Disclosure: Dr. Robert Bosch was kind enough to send me a copy of Opt Art for no charge.
If not a love, at least an appreciation for mathematics is, I think, important to take the most out of Opt Art. The mathematics isn't difficult, but the variables can be a lot to keep track of if you're not used to dealing with them. That said, Dr. Bosch's explanations are written with simple, accessible terms that make the barrier less imposing for the less mathematically-inclined.
The most difficult chapter for me to follow was the sixth, "From the TSP to Continuous Line Drawings," especially once I reached the branch-and-cut section. However, the TSP art pieces were also among my favorites! I was inspired at many points to shut the book and try some of these visual design problems myself. I'd definitely recommend Opt Art to my more math-favorable friends.
Disclosure: Dr. Robert Bosch was kind enough to send me a copy of Opt Art for no charge.
January 11, 2024
Lots of information, I will definitely be referring back to this book as I like to do things at the intersection of maths and art too. There were some really good ideas. I loved the TSP hand drawing dots, and the use of the adjacent country colouring problem to make approximations more interesting.
I agree with another reviewer that the book would be improved if the author had used open source tools and made the code available.
Also there was a lot more discussion of the maths than the art - a lot of the works were charming but some were not so beautiful or artistic - more discussion of the artistic merits of the works would have been nice. And a lot of the work in the book was based on adapting existing images rather than creating brand new images.
I agree with another reviewer that the book would be improved if the author had used open source tools and made the code available.
Also there was a lot more discussion of the maths than the art - a lot of the works were charming but some were not so beautiful or artistic - more discussion of the artistic merits of the works would have been nice. And a lot of the work in the book was based on adapting existing images rather than creating brand new images.
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March 29, 2020Great book!
The author presents its work using mathematical programming to create art. I really enjoyed and also I reproduce some of the examples presented in the book.
The author presents its work using mathematical programming to create art. I really enjoyed and also I reproduce some of the examples presented in the book.
February 12, 2021
I have no words other than "Maths have never been so optimally beautiful". A great tutorial book to learn from the best in opt-art and unlock your creativity.
Displaying 1 - 7 of 7 reviews