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Playing With The Flow of Pi, e, and Phi

Before continuing, look at the Recommended Resource Review for this week first. It will provide a context and motivation for the website discussed below.

This wonderful artwork has been created by Canadian scientist Christian Ilies Vasile, then expanded by Martin Kryzwinski. The artwork is created using the data visualization software Circos. The result shown in Resource section is a beautiful and colorful visual representation of the mathematical constant π (pi).

Go to Kryzwinski's website to see the full process, plus a video showing the "flow" of pi.

Now, what happens if you repeat the process using the other famous constants of e and phi?

They also created artwok by color-counting the number's digits as they are found next to each other, i.e. the ones with various sized dots show how often digits are found next to each other. They even discuss interesting probabilities of digit sequences, such as the appearance of six 9's in the pi-string. For example, they estimate that it is 50-50 that in a 69,000 digit random sequence, one will find a run of 6 identical digits.

Also, the two scientists built bead-like rosettes representing pairs of digits with an additional coordinate based on their order (so some out-of-order order).

And finally, they mapped the ten digits onto a red-yellow-blue Brewer palette, applied to an Archimedean spiral (defined as r = a + bθ). Again, see the results on their web site. Fun, creative stuff!