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Visualizing the Infinite Beauty of Pi and Other Numbers

Math and art may appear, superficially, like two disparate fields, but they’ve been in conversation for millennia. One recent example of the synergistic possibilities between the two comes from Canadian scientists Christian Ilies Vasile and Martin Kryzwinski. The pair have utilized the data visualization software Circos to create beautiful and colorful visual representations of mathematical constants π (pi), φ (phi), and eusing transition probabilities and color-coded digits on Archimedean spirals.

Given the endless nature of π, φ andethe task of representing them visually in a simplified form could seem daunting. However, thanks to new infographic technology and the natural form of the Archimedean spiral understanding pi’s sequencing (for the layperson anyway) becomes a thing of beauty rather than outright confusion—the technicolored vastness evoking an almost spiritual quality.

For the technical deets on how the pair created the visuals, check out the project page on Kryzwinski’s site.

Photos shown:

Progression of the first 10,000 digits of π By Cristian Ilies Vasile.

Progression and transition for the first 1,000 digits of e.

Progression and transition for the first 1,000 digits of π, φ and e.

Progression and transition for the first 2,000 digits of e.

Progression and transition for the first 1,000 digits of the accidental similarity number.

Progression and transition for the first 1,000 digits of φ.

Numbers like π (pi), φ (phi), and e are inherently free of patterns.

As a quantity to themselves, they represent a specific, finite relationship between two measurements, such as the ratio of a circle’s circumference to its diameter. Yet, pull on the thread and those numerical tapestries unravel into an irrational soup of nonrepeating chaos, a true example of randomness.

That doesn’t mean they don’t make great visualizations, though. Christian Ilies Vasile and Martin Kryzwinski converted these numbers into the beautiful representations above.

The techniques are a little complicated, but the ones with lines bascially represent pairs of digits as they are found next to each other, the ones with various sized dots show how often digits are found next to each other, and the bead-like rosettes represent pairs of digits with an additional coordinate based on their order (so some out-of-order order).

You really don’t want to miss their Archimedean spiral, either:

To dig in to the tech a little more, visit their website. This kind of thing is readily doable with today’s software, so get crackin’!

(Via The Creators Project and myampgoesto11)