Since 2013, scientist and data graphics guru Martin Krzywinski, who is both a scientist and data artist, has been celebrating “Pi Day” by visualizing the outstanding mathematical value in original and fascinating ways. This year, inspired by the recent announcement of the discovery of gravitational waves by LIGO scientists, Martin has dropped a complex new variable into his latest visualization: gravity.

Like the interaction of physical masses, this visualization is governed by a set of laws. It starts with the first *n* digits of pi, each represented by a colored dot and arranged in a circle. The color of each digit signifies its value based on a rainbow scale of magenta to violet. The value of *n *could be anything, from three (3, 1, 4) to 1,000. Each digit is assigned a mass according to a mathematical formula including a second variable,*k*. The interactions of the masses are then visualized as paths connecting them. At times, masses come to orbit each other; in other instances they collide, coalescing into a larger mass whose increased gravity intensifies its impact on the other bodies around it.

Depending on the respective values of *n* and *k*, the visualization experiences various permutations. As the values increase, the interplay of forces becomes more dramatic and complex, the path winding and looping around itself, often breaking the bounds of the circle and veering into graphical oblivion. In some instances, as in the one below, all the digits eventually collide into a single mass within the circle.

Evidently, Krzywinski’s work is not the only one relevant Pi Day visualizations. Nadieh Bremer, another scientist-turned-data-visualizer, responded in 2015 with her own Pi-based graphic. In honor of Pi Approximation Day (July 22nd, also denoted as 22/7, a fraction that is about equal to pi), here are a few snapshots of Bremer’s work.

The central premise here, as signified quite elegantly in the legend above the first iteration of the graphic, is that each successive digit of pi is visualized as one “step” in a different direction. The visualization becomes increasingly dense and convoluted as more digits of pi are added. And interestingly, somewhere between 1,000 and 10,000 digits, the configuration seemingly begins to mimic certain natural structures, like intricately folded proteins or crystal formations. As is so often the case when data and art come together, Bremer’s work is as surprising and complex as it is beautiful.

Visit Martin’s website to read more about his process and see other variations on the visualization.

# References

[1] “The boundless beauty of Pi” post written by Amanda Montañez from the Scientific American Blog

[2] “The Gravity of Pi” post written by Amanda Montañez from the Scientific American blog.

[3] Martin’s website .

[4] Visual Cinnamon portfolio.