Hello Brian and Pilou,
Thanks for sharing the video - great stuff, but it took a while till I understood it.
So like Brian I can't withstand and so I made also some experiments. I started with a expansion factor k is for the main curves given by the construction of the golden spiral. For a 1/4 turn the golden number = r = exp(k*PI/2) -> k=4*log((sqrt(5)+1)/2)/(2*PI) Ok - that's not new and already known by WIKI and the rest of the world. But it's not necessarily.
But I didn't find that:
If you use this k_1 for the main spirals e.g. 13 and have 8 counterclockwise ones, you can use a k_2=k_1/golden number. I think that's the best choice, because you get a minimal distorted element. What do you think about?



Have a nice day
Karsten