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@Sio, Heavy math.
Thanks for sharing! I’m starting to get acquainted with the subject.
My idea was that the pattern on the map should tell you when you’ve got the right lines drawn.
Once I had drawn all the lines at the end of Clue 9, I had an owl on the map. left side straight lines and right side blur or fractal as it was the French border.
As I turned the map north, I saw a capital B, or B I, with an arrow.
Then I re-read Clue 2: ‘My fifth is in rage’ and Clue 4: ‘When he is lying down my fifth hums (or ronfle)’. I wanted to get the letter N or Z on the map and something furious.
I looked at a visual with BAGFEDC and connected the cities in that order: Bourges-Angers-Gerardmer-Forbach-Epernay-Dieppe-Cherbourg. Now I had half of the Fermat spiral. I completed it by combining: Bourges-Hericourt-Issoire-Jarnac. Now I had the Fermat spiral on the map. In addition, the pattern looked like a wild boar or mad dog with an eye in Paris and an ear in Bretagne. And now I had N or Z on the map.
However, the arrow is still detached and unconnected to the rest of the pattern, but now I got instructions to orient the arrow.
After that, I thought that if I connect the cities in order: 0-10, the pattern on the map resembles a flame. The flame can rage or hum, so it matches Clue 2 and Clue 4.
An interesting game. It’s up to you which way you choose.