They actually do have a relationship to Phi, but not the one in the in picture you link, which is obviously bad.
If you draw a pattern of dots according by rotating points 137.5 degrees (which you see on a lot of seed heads and fruits, such as sunflowers, pineapples, pine cones, romanesco broccoli, various succulents, etc.), you create a pattern were certain spirals 'jump out' at you. If you count the number of 'arms' in each successive set of spirals, the numbers are the Fibonacci sequence. http://momath.org/home/fibonacci-numbers-of-sunflower-seed-s...
Somewhere along the line I read on some website that it might have to do with optimal packing theory -- distributing the maximum number of seeds over the seedhead, but I think it was just a guess. It does seem to show up in a variety of plants, more than just chance would lead you to expect.
If you draw a pattern of dots according by rotating points 137.5 degrees (which you see on a lot of seed heads and fruits, such as sunflowers, pineapples, pine cones, romanesco broccoli, various succulents, etc.), you create a pattern were certain spirals 'jump out' at you. If you count the number of 'arms' in each successive set of spirals, the numbers are the Fibonacci sequence. http://momath.org/home/fibonacci-numbers-of-sunflower-seed-s...
Somewhere along the line I read on some website that it might have to do with optimal packing theory -- distributing the maximum number of seeds over the seedhead, but I think it was just a guess. It does seem to show up in a variety of plants, more than just chance would lead you to expect.