The formula is probably simpler than it looks

All lines drawn never intersect—only touch.

1. Draw any number of straight lines at any angle to any length.
2. From any point on those lines draw new straight lines perpendicular to the initial lines, continuing until the new line touches another line
3. Repeat step 2 for each new generation of lines, keeping in mind to continue the line…
   1. Until it touches another line
      OR
   2. Until it reaches a point where it is perpendicular to a line from the generation before the previous one.
4. Stop the process when you are satisfied with the composition

   [image scan pending]