Doyle Spiral (2,12)

Here is a study on Doyle spiral

Doyle spiral - Wikipedia

 

Hexagonal circle packings (josleys.com)

not a lot of explanation on the internet... is it  trivial?...I confess that I found it tough to understand

here is my methodo in Xgen/GGR

1. define the 3 base circles (1, A, B)

  • I do it manually for a given set of (p,q): (2,12) -> tuning "a , t , r" parameters in the 3dxml
  • you can find automatic ways in python or other languages. I need to check if possible to do it in Xgen / GGR -> would like other pairs

2. define the remaining base flower (B/A, 1/A, 1/B, B/A)

3. create the outer big spiral from A and B

4 create the inner smaller spiral from B and B/A

  • in the model, I dont use it because too small
  • however it will be usefull for the "double spiral" (spoiler) on a different post

5 create the center spirals

6 slice the disk with the spirals

7 set the colors