Here is a DoubleDoyleDemo2 spiral, made from nodes, with two attractor points, x = -1 and x = +1.
(Code from Robin Houston was used.)

x=-1 is the regular Doyle attractor, moved from 0 to -1.
x=+1 attractor point represents infinity.

The 4 Macros used were:
1. ConvertCenters.nod (creates 3 points on each existing Doyle circle.)

2. MoebiusTr_0_1_inf_to_neg1_0_1.nod (Moebius transform maps x=0 to x=-1,
maps x=1 to x=0, and maps x=infinity to x=+1. This formula is then applied to all of the 3_point circle points. The mapped sets of 3 points are then run through the MoI's 3_point circle node. One extra step is to get the center Y value of each mapped circle, and mask out those circle which have absolute value greater than 5.5. (The value is supposed to be 10, but the math seems to be working wrong...) This gets rid of huge circles, and two very large circles which appear to be incorrect, for unknown reason.
(Mapped circles are produced, because (extended) circles are mapped to (extended) circles, by the moebius transform.) Note Pilou's video post. The moebius transform represents reverse stereographic projection to a sphere, rotation of the sphere by 90 degrees with a certain axis, and then stereographic projection back to the MoI Top View.
It is sufficient to only map 3 points per original circle.

3. Extract_XY node. This converts a pointarray point into a Duo-numarray, representing a complex number.

4. Extract_2XY nod macro. Same as #3, with two point inputs, and outputs X1 Y1 X2 Y2,

Place the 4 Macros in the Macros folder.
Run the DoubleDoyleDemo2.nod.
(Assumes that DoyleSpiral.js and doylefn.js are already in the extension folder of nodeeditor.)

One other point. The math.hypot may be better and less error prone that the current formula for hypotenuse. (Not tried yet.)

Thing would look much better with colors and planar...

The maxModulus and minModulus were adjusted so that the neighborhood of the two attractor points looked about the same.

Modifying to more extreme values may hang up the computer, but on windows 10, MoI can be closed in Task Manager.