This is the fourth and final piece in my yarnbombing project at the community bike store in Cobden Road, Brighton. The other three seasonal pieces are the autumn tree, winter hat dispenser and spring swifts.
The centre of the sunflower shows the fibonacci spirals that can be seen in real sunflowers. The chart I used to construct this piece is below, with my markings. This diagram came from this lovely website, which is worth exploring if this kind of thing interests you.
Sunflowers create this pattern by producing each new seed at the centre. As each seed grows, it pushes its way outwards and occupies space that is as far as possible from the surrounding seeds. This process naturally results in an arrangement of seeds that can be artificially generated using this formula:
radius = c * sqrt(n)
angle = n * 137.5
where n is the index number of the seed and c is a constant scaling factor. I found the formula here, but the author of that page credits it to H. Vogel, whose 1979 article A
better way to construct the sunflower head (Mathematical Bioscience 44, 179-189) does not appear to be available online.
I began at point 1 and worked a chain outwards along the yellow line that passes through points 14, 27, 40, 53 (adding 13 each time), then switches to adding 34 each time to pass through points 87, 121, 155, 189, 223, 257, 291. There is one spacing chain between each chain for a numbered point.
From point 291 I worked my way back to the centre, starting by subtracting 21 each time (270, 249, 228, 207, 186, 165, 144, 123, 102, 81, 60, 39, 18), then subtracting 8 (10, 2).
I carried on in this way, forming all the yellow lines and working into existing stitches as I came across them. Then repeated the process with the pink lines, and finally the blue lines, which had to be done one at a time.