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This diagram plots every irreducible fraction between 0 and 1 as points, where a point's x coordinate is the fraction's value (from 0 to 1) and its y coordinate is the fraction's denominator (from 2 to whatever the maximum is).

Denominators for denominators from 2 to 20

The diagram for denominators up to 100

It makes really nice patterns the further the denominators go and I'd really like to know more about it. I think I remember finding it on Wikipedia or something a long time ago with a name along the lines of "the stars of x" or "the towers of y".

Maybe it's just nothing, though.

David G. Stork
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dino
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    The $y$-value looks like it's the negative of the denominator? Or else the diagram is drawn "computer style" with x increasing from left to right and y increasing from top to bottom. – Misha Lavrov Feb 16 '21 at 20:34
  • one possibility https://en.wikipedia.org/wiki/Farey_sequence – Will Jagy Feb 16 '21 at 20:49
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    @MishaLavrov right, it seems to be Farey denominators, upside down from the plots on wikipedia I think one can click directly on this image link: https://en.wikipedia.org/wiki/Farey_sequence#/media/File:Farey_sequence_denominators_25.svg – Will Jagy Feb 16 '21 at 20:56
  • @MishaLavrov Yes, that's right, I forgot to mention that – dino Feb 16 '21 at 20:57

1 Answers1

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This is the graph of the reciprocal of Thomae's function.

https://en.wikipedia.org/wiki/Thomae's_function

Karan Elangovan
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