Complex circle spiral

Ideas
1
Open in Wolfram Cloud ↗
3 Likes
2

Looks a bit like Ford circles over Farey fractions

fordCircles[n_]:=Map[{{#,1/(2 Denominator[#]^2)},1/(2 Denominator[#]^2)}&,FareySequence[n]]

fordCirclesGraph[n_]:=Graphics[
  Map[Circle@@fordCircles[n][[#]]&,Range@Length@fordCircles[n]],
  PlotRange->{{0,1},{Automatic,0.5}}
]

Fordcircles.png
Fordcircles.png466×272 9.77 KB

3

Turns out this is the 1-4 Doyle Spiral.

Doyle14.png
Doyle14.png160×140 5.04 KB

Here’s the 1-5 spiral.

Doyle15.png
Doyle15.png254×197 10.1 KB

The whole series seems to have unusual symmetry polynomials.