This image here shows a beautiful fractal-like image. Does this map some sort of function, each number corresponding to a section/colour? Or is this just pretty art? Thanks!



closed as off-topic by Mark Viola, Zain Patel, vonbrand, Daniel, user99914 Jul 23 '15 at 18:21

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  • "This question is not about mathematics, within the scope defined in the help center." – Mark Viola, Zain Patel, Community
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  • 1
    $\begingroup$ It looks like a network plot. There are many nodes on the perimeter and the color curves are the links between nodes. A computer visualization program can plot them. $\endgroup$ – Yan King Yin Jul 23 '15 at 5:19
  • 4
    $\begingroup$ Yes, that circles with a lot of internal arcs look cool. Also it represents the duality of man and the futility of human endeavor. $\endgroup$ – Asaf Karagila Jul 23 '15 at 5:26
  • $\begingroup$ Where did this image come from? The context could be helpful, and anyway, sources should be credited. $\endgroup$ – Nate Eldredge Jul 23 '15 at 5:49
  • $\begingroup$ @NateEldredge My friend sent it to me >_< I don't know where he got it. $\endgroup$ – Conor O'Brien Jul 23 '15 at 12:25
  • $\begingroup$ I found this for you. I searched for this thread. This video has the answer for your question youtube.com/watch?v=NPoj8lk9Fo4 $\endgroup$ – AmerYR Jul 24 '15 at 9:12

This image represents the progression of the first $10,000$ digits of $\pi$, and was produced by Cristian Ilies Vasile using the software Circos (or so a Google search tells me).

To elaborate on this, since $\pi$ begins $3.14159\ldots$, you would begin to form this image by first adding an edge/arc from $3$ to $1$, then $1$ to $4$, then $4$ to $1$, and so on.

You can see this image as related to the question of if $\pi$ is a normal number, which is still unknown. Roughly speaking, a number is normal if it's digit progressions of all lengths are 'random,' in the sense that all finite digit progressions of a given length occur with equal frequency. For this image, that would mean that there are a roughly equal number of edges leading from any one node to any other node (and also from any node to itself, but I don't see those edges drawn).


The method used to generate this image using the digits of $\pi$ is described here.

I disagree with your characterization of the image as "fractal-like".

  • $\begingroup$ Fractal-like, meaning, it is reminiscent of a fractal for me, not necessarily a fractal. $\endgroup$ – Conor O'Brien Jul 23 '15 at 12:24

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