Name of this type of plot? Does anyone know how to produce it

Question

Does this type of polar plot have a name? Does anyone know how to produce it in octave 3.8.1 which is compatible with matlab?

Link to site

Answer 1

The picture you are showing appears to be one from Cristian Vasile. I believe the one you have shown is "Flow Of Life Flow Of Pi"

"The art of Pi" by Martin Krzywinski is a similar piece of artwork, He has similar images for $e$ and $\phi$. On that linked page it mentions that he created his images using the free, open source (GPL) "Circos" data visualization software package that he maintains, and has a page describing the mathematical methods used to create it, and how he modified Vasile's method slightly to create his versions, specifically adding outer rings to identify the frequency of certain number repetitions and pairings. (He specifically highlights the 99999 that occurs at position 762).

From his descriptions of Vasile's method, describes the process as jumping from number to number in the order of the digits in $\pi$. Thus, for 3.14159, it starts at the most counterclockwise position on 3, then follows an arc to 1, where it lands at position 2, then it arcs to 4, where it lands at position 3, etc. The actual locations of positions 1,2,3, etc, appear to be relative to the number of digits calculated. Hence, if you calculated 100 digits of $\pi$, each number would have 100 "landing spots" for each arc. I believe the image you linked uses 10,000 digits.

The sweep of the arc not described, but except for adjacent digits the arcs all appear to be circular (constant radius), which creates the apparent concentric rings near the center where the arcs peak. The outermost ring, created by adjacent digits, appears to be made using elliptical arcs.

The colors on the arcs are simple gradients from one digit color to the other.

As the Circos code is free, open source software licensed under the GPL, anyone is free to view the source code and copy the mathematical algorithms.

I don't believe anyone has generated a Matlab or Octave codeset to generate similar graphics. It should be possible, however the most difficulty will probably be in mapping the proper outward facing circular arcs onto a polar map. It would require some apparently nontrivial trigonometry. I have also not seen gradients in plotlines in either gnuplot or fltk graphics options.

Answer 2

This is not actually a polar graph: it represents the digits of pi, where a line is drawn to each successive digit. I don't know that this would be easy to generate in either matlab or octave; getting the patterns shown here would depend very sensitively on the algorithm for determining the endpoint of each line within the block of color.