UNIVERSITY PARK, Pa. — Venkatraman Gopalan, professor of materials science and engineering and physics at Penn State, remembers fondly the tidy, patterned shapes called "kolams" that adorned the entrances of homes in Southern India. The ancient practice of drawing symmetrical patterns which snake around a grid of dots, also called "pulli kolam" in Tamil language, is drawn daily by millions conventionally using rice flour.

The practice signals well-being and a promising start to the day. The kolam disappears as ants and birds feast on the fresh rice flour, clearing it for a new kolam the next morning. Besides their beauty, Gopalan said, he was attracted to the underlying mathematical structure of kolams.

Kolams also caught the attention of Amy Alznauer, a children’s book author and math lecturer at Northwestern University. She used kolam patterns in illustrations for her 2020 book, “The Boy Who Dreamed of Infinity,” which chronicles the life of Indian math genius Srinivasa Ramanujan. Despite dying at age 32 and receiving no formal training in pure math, Ramanujan made numerous brilliant contributions to the field.

Like kolams themselves, the circuitous paths of these two educators connected, leading to a partnership to promote kolams to the masses, especially children. They created the game Kolam Tiles, available in maple-wood-cut and digital forms, as a way for people to explore this blend of art and geometry.

While researching for her book, Alznauer came across a video that Gopalan — who researches the symmetrical pattern of crystals at Penn State —  had made showing how complex kolam patterns can be created using symmetry. By breaking these patterns down into a small number of puzzle pieces, he said, one can connect them together with some simple rules to create highly complex kolams that are otherwise very difficult to create. The symmetrical patterns explored in the game aren’t dissimilar from the crystalline structures he researches at UNLOC, the Ultrafast Nonlinear Optical Characterization Group, said Gopalan.

Kolam Tiles at present consists of six different shapes centered around a dot. The goal is to stack the shapes to form patterns with no loose ends. All the tiles must connect to complete a pattern of continuous loops of lines around the grid of dots. Players can challenge themselves by seeing how many different kolams they can create or challenging others to create the same kolam. They can also try one of Gopalan’s puzzles, which he frequently posts to YouTube under the banner "Kolam Crossing."

“The six types of tiles are the basic building blocks, almost like Lego pieces with which you can form bigger and bigger kolams. One can create 1 septillion kolams (1 followed by 24 zeros) on just a 4x4 grid of dots, which is an estimate for the number of stars in our universe,” Gopalan said.

Alznauer reached out to Gopalan in 2020 and later her own industry ties for help to create the physical and digital versions after discovering Gopalan shared her same passions for kolams and education.

“It was clear to me that Venkat had a family connection to kolams and was approaching it from a place of deep familial awareness and love,” Alznauer said. “He’s a symmetry expert and had taken all of that expertise into thinking about kolams, which was very exciting. He just seemed like a great teacher and wonderful person. He was someone I wanted to work with.”

Gopalan was equally impressed.

“Amy's life story is very coherent and meaningful, with great love for the mathematics of Ramanujam and the cultural context in which he flourished,” Gopalan said. “Her life as a children’s author and educator told me she would approach kolams, too, in a meaningful way. From the first time talking with Amy, I knew she was a very energetic and passionate person. I knew it would be a great collaboration, and it has been so.”