Hi Mindset,

Pilou made an excellent tutorial.

Assuming the initial 3 circles are in the coherent ratio, for maintaining radius ratios, i.e. to maintain external tangency, without circle overlap, the third circle selected would be the circle tangent in the opposite cleft.
Selecting a different 3rd circle, of different radius from the opposite circle, may be done at the whim of the user, but the resulting new circle will not maintain the coherency.

Spirals start with the circle centered at (1,0). To make a spiral with this script, to add one circle to the spiral, it is necessary to make two new circles, (usually), in order to have the helper circle for the next spiral circle. If p = q is used to set up coherence, with a 3rd party solver, the "spirals" are actually rings of circles, kind of like a spiral without curvature.

- Brian

After creating the new circle, right click will re-activate the Doyle flower script. (Pilou mentioned this "recall the function".)

Also after creating the new circle, it might be nice to have a deselectAll added to the Doyle flower script, but it is not essential.

A new script would automatically create the whole Doyle spiral, given user input parameters, with a few lines of code. Yet to be written or adapted from the abstruse mathematica code, to javascript. I'll work some more on a new script, after the bookkeeping gets done:-)
(Powers of the A (or B) circle centerpoint, as complex numbers, create spirals of center points of circles.)

Notepad++ prefers centre to center:-)

- Brian

It is amazing to me that a few simple circles have let to the many abstruse mathematical papers on the subject.