*This week’s blog entry is written by Jenya Doudareva, an MASc student at Centre for Research in Healthcare Engineering and a literature, art, and music aficionado. You can reach her at jenyadoudareva [at] gmail [dot] com.*

The previous entries have set up OR to be serious business. With applications ranging from military, supply chain management to finance, and even to healthcare and medicine, it is clear that OR has a lot to offer to the world. Personally, I find such diversity of a discipline to be refreshing and alive…creative even. To see that a problem in healthcare and a completely different problem in finance can be modelled using the same underlying principles is astounding.

However, going back to creativity in its more traditional sense – one could ask, can OR be of any use outside of the “serious” disciplines? Does OR have anything in common with art? I certainly have asked this question to myself a lot, since I only pretend to be a serious and professional person.

The answer to these questions, one could be compelled to assume, would be a stern “no”. Such answer would make sense to people who firmly believe that art and science have nothing to offer to each other, and that their values are opposite. However, if you, like myself, believe that the guiding principle behind artistic and scientific thought is the discovery of something new, the yearning to express the world around us in a way that is more understandable and more relatable – then you might have a hunch that OR techniques can be out there right now, with the artists.

Obviously, I am about to state that ‘yes, indeed!’ there are a few very impressive and nifty ways in which people have applied OR to their artistic expression.

**Exhibit 1: Domino Artwork**

There exists a little group of people who are obsessed with making pictures out of dominoes. How do they create the images or Mona Lisa, or Lincoln… or anything really, out of dominoes? You would never guess – they use Integer Programming (IP)! From their website:

We use a mathematical technique called integer programming to find the best way to position the dominoes. For decades, integer programming has been used by Operations Research professionals to construct schedules, devise routes, and solve numerous other large-scale planning problems. Over the years, it has saved corporations millions of dollars. And now it is being used to make artwork!

**Exhibit 2: A Mathematical Art Exhibit **

As the artists have already mentioned, IP is a specific OR technique. More precisely, IP is an optimization technique in which some or all of the variable are restricted to be integers. Now, would anyone like to discuss how exactly is IP used by the Domino Artists? Any idea? You are welcome to post your guesses in comments to this entry.

The mathematical art exhibit is a very cool concept. It happens annually, and last year, for example, more than 250 mathematicians from around the world attended this meeting. Mathematics and the Arts was one of the sessions that was organized by Michael J. Field (who was also a conference keynote speaker) from the University of Houston, Gary Greenfield (who is the Editor of the Journal of Mathematics and the Arts, Taylor & Francis) from the host university, and Reza Sarhangi, the author, from Towson University, Maryland. Last year the winner was Bob Bosch, who described his work as follows:

I began by converting a drawing of a two-component link into a symmetric collection of points. By treating the points as the cities of a Travelling Salesman Problem and adding constraints that forced the salesman’s tour to be symmetric, I constructed a symmetric simple-closed curve that divides the plane into two pieces: inside and outside. With a water jet cutter, I cut along this Jordan curve through quarter-inch thick, six-inch diameter disks of steel and brass. By swapping inside pieces I obtained two copies of the sculpture. Here, steel is inside and brass is outside… After I get an idea for a piece, I translate the idea into a mathematical optimization problem. I then solve the problem, render the solution, and see if I’m pleased with the result. If I am, I stop. If not, I revise the mathematical optimization problem, solve it, render its solution, and examine it. Often, I need to go through many iterations to end up with a piece that pleases me. I do this out of a love of mathematical optimization–the theory, the algorithms, the numerous applications.

Now, how amazing is that? How would you use your OR expertise to create something fun, interesting, and perhaps breathtaking?

P.S. Special thanks to Michael Trick’s OR blog for a discussion of wide variety of OR-related topics.

On a related note: I recently came across Origami using mathemetics on TED talks. Robert Lang, the speaker, basically uses circle packing to generate folds and create really complex crease patterns. Amazing! http://www.ted.com/talks/robert_lang_folds_way_new_origami.html