What if you could hear how a limb grows? With this project, you can

Biologists, mathematicians, illustrators and musicians came together at Northeastern for a peculiar project. Using data on how limbs grow, they transformed complex biology into music.

“Morphogenesis” combines illustrations, music, math and biology to transform the process of limb growth into a mixed media art project. Courtesy of Sandra Shefelbine

Sometimes inspiration comes from the most unlikely of places. For musician Garrett Compston, it came in the form of a skeleton.

Alongside scientists, engineers and illustrators, Compston, a musical technology student at Northeastern University, transformed the mathematical equations and biological concepts behind how limbs grow into a nearly six-minute piece of music. 

Titled “Morphogenesis,” after the biological process behind how individual cells, tissues and organs develop their specific shapes and structures when the embryo is still developing, the project, helmed by faculty and students at Northeastern, blends math, biology and music. Although it started as a fun exercise for the academics involved, this interdisciplinary project gradually became an exercise in something scientists can struggle with: translating complex, important ideas to the public.

“If we’re trying to convey what we’re doing … we can’t just sit in our ivory tower and do our thing,” said Sandra Shefelbine, a professor of bioengineering and mechanical and industrial engineering at Northeastern who helped lead the project. 

“Using a different medium helps us to translate pretty technical things into something an audience can get a conceptual grasp on. In this case, “Most people don’t think in math,” Shefelbine added. “But they can hear it [represented in music].” 

The work it took to make music out of math didn’t come easily, but the team developed “Morphogenesis” with joy and genuine curiosity.

Math and music have a long, tangled history, as do math and biology. The ancient Greek mathematician Pythagoras discovered that musical harmonies were made possible by simple mathematical ratios. A few centuries later, building on the work of those who came before him, Renaissance man Leonardo da Vinci utilized mathematical modeling to comprehend human anatomy and physiology, dissecting the human body’s appearance and functions into distinct patterns. 

But the Northeastern team took inspiration for their project from a more recent historical figure: The 20th century mathematician and computer scientist Alan Turing. 

Among his many contributions, Turing is credited with a concept that helps explain how natural, asymmetric patterns, like the spots on a leopard or even how different parts of our body, develop from a symmetrical embryo. Turing surmised that these repeating patterns come about when a chemical system — in the case of development, hormones or genes — that would otherwise have a stabilizing effect on the body causes instability. Laws of physics dictate that all systems tend to want to return to a state of stability, which is where patterning — like on fish skin or how limbs develop — takes root. This concept is now known as a Turing pattern. 

This process helps explain limb growth across the animal kingdom, Shefelbine explained. Humans, bats, whales and even axolotls — the pink, smiling salamanders that Shefelbine studies due to their regenerative ability — all have the same limb structure: a single bone connected at the shoulder, two bones in the middle and many bones where the digits, or fingers, form.

“We think that the way that these develop is a Turing pattern, and it’s a Turing pattern in all species,” Shefelbine said.

That understanding served as the foundation for Compston’s music, which focused on representing the biological process behind limb development. 

When a limb first starts to grow, it’s a homogenous “bag of cells,” Shefelbine explained. But as the limb develops, those cells take on unique functions and help to form different parts of the limb. Their role is established from the beginning of the process, a concept known as cell destiny, but they don’t step on stage until they’re ready to play their part.

“The whole project is about fate, how cells decide that they are going to build this very complex structure even though the structure is way bigger than they are,” mechanical engineering Ph.D. candidate Soha Ben Tahar said. 

Beyond biological systems, Tahar also grew intrigued by the similarities between how Turing patterns can be applied to something like sound vibrations.

A vibrating soundwave works like a simple pattern that, when repeated, forms a Turing pattern, according to Ben Tahar. Combining enough of those vibrations makes the sound that’s heard when a string is plucked or a flute is played. Different combinations of these vibrations, create different timbres, the unique sonic character that makes every instrument or voice sound unique.

“To me, the magic of math is that at the end of the day all equations look alike,” Ben Tahar said. “Using this same tool for two very different processes, that was the bridge that we built.”

To mimic the process of cell destiny sonically, Compston, along with Victor Zappi, an assistant professor of music at Northeastern, synced mathematical values that Ben Tahar generated from equations used to model Turing patterns to waveforms. Like with any Turing pattern, Compston could then combine the individual frequencies from each singular waveform to create a new sound that evokes a synthesizer. The electronic composition begins as a series of single notes played one after another, but over time more sounds get layered in. Similar to an orchestra starting with a single player and building with additional instrumentation, Compston created an increasingly complex sequenced pattern that still has the initial notes at its base. Similarly, there are no traditional melodies in the composition to represent the pattern-based math he was drawing on. 

It’s not a purely one-to-one representation of the math but instead a creative reinterpretation, Compston said, adding that music based purely on the mathematical equations would have been accurate but so abstract that it could be offputting to an audience. 
In the final composition, he takes all those sounds, which are still based on Ben Tahar’s math, and layers them to create a sonic representation of how limbs grow. The final piece sounds like a series of synthesized church bells that grows in complexity until it reaches a crescendo of melodies that bounce off one another.

All of these sounds are layered over an animated video of an axolotl limb growing over time. Created by splicing together 1,500 hand-drawn charcoal illustrations made by artist Alan Dursee for the project, the animation is a representation of limb growth, while the music adds an abstracted layer that conveys the same idea.

“I [created] a lot more patterns that would evolve over time, leaning a lot on [sequences of notes] and things in musical language to be a little more abstract with where to find the melody and where to find the driving force of the piece,” Compston said.

It ultimately took nearly eight months to complete “Morphogenesis,” which only begins to scratch the surface of the vital role played by the Turing patterns that Shefelbine and her colleagues are researching. But if a picture is worth 1,000 words, then the project’s combination of audio and visual art multiplies the word count 10-fold.

For Shefelbine, the project might not be saving lives, but it’s emblematic of the kind of work that can happen when people from different backgrounds, academic or otherwise, come together. 

“They had very different toolboxes, very different ways of approaching the world and understanding the world, and they had to explain their way of understanding it to somebody who had a different toolbox,” Shefelbine said. “That’s really powerful.”