As you already know I have been exploring geometric drawing with the ultimate goal of using these images in finished paintings. l plan on combining the geometry with my figures and/or launching into purely abstract works. A couple of weeks ago I decided to try opposing Fibonacci spirals. You've seen them in the heads of flowers, pine cones, pineapples and the really cool romanesco vegetable. I didn't think it would be too hard. I'd focus, accept some trial and error, focus some more and I'd get it. It turned out to be a fairly harrowing experience, with mind bending twists and turns (pun intended), frustrations that caused marital problems, grouchiness, and general malaise until I figured it all out. See the dramatic pictoral journey recreated here.
The Fibonacci sequence (1, 1, 2, 3, 5, 8, 13...) dictates the size of the squares that are used to draw the arcs. These drawings are actually a close approximation of the patterns we see in nature as an exact replication is not possible. What is interesting to note is that the websites and video tutorials that I found showed the spiral starting with two small squares. When I did multiple spirals this way the arms crossed. I ended up skipping one, so I did the # 1 square once, not twice, and spaced it out a bit from the center. I believe the actual way to do it would be to split the golden rectangle into a square and draw an arc, and keep doing that ad infinitum. Recommended books: Ruler and Compass by Andrew Sutton, Sacred Geometry by Stephen Skinner.