Click flag. Kathy painted the sunflower over top of the spirals I generated with code. Then I put her painting in the background and overlaid the spiraling, migrating florets again. See many patterns of spirals emerge in the Sunflower. The ratio of the total clockwise to the total counterclockwise spirals approximates the golden ratio. That translates to an angle of 137.5 degrees. The angle that best fills the space is 137.5 degrees, which is the "golden angle." You can try other angles. Even just 137 degrees or 138 degrees produces big gaps between spirals.
The florets change from greenish to more orange as they grow older and move (with just one short line of code). We use clones that move out from the center. Each successive clone moves at the golden angle (137.5 degrees) relative to the previously created clone. Each clone represents a floret that starts from the center, then migrates outwards, growing slightly as it moves. The golden angle turn of 137.5 degrees is the best way to fill space, and causes the number of clockwise and counterclockwise spirals to be Fibonacci numbers (such as 5, 8, 13, 21, 34, 55, 89, 144....). (We kill off clones once they are far from center. This allows us to bypass the clone number limit in Scratch, so we can continuously create new clones) Sunflowers, daisies and other flowers have this type of spiral patterns. We produced the very similar programs in Python and NetLogo to provide a comparison: https://lifepatternsemerging.com/spirals This is part of our beautiful discovery box on floral spirals, along with a sunflower drawing lesson. See also our Scratch model using colors to mark off spirals, and another Scratch model using a pen rather than moving clones.
