Choose number of colors, click flag. After reaching the Scratch limit of clones (300), we "stamp" their picture, the code kills all clones (300 diamond shaped florets) and creates new ones. The result is spirals with many more diamond florets than otherwise possible. Altering number of colors highlights different spiral patterns. 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 colors help you see many different spiral patterns, some clockwise, others counterclockwise. You can create hybrid patterns by changing the number of colors every few seconds. 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....). Altering number of colors highlights different spiral patterns. (After reaching the Scratch limit of clones (300), we let them expand outwards a bit, leaving a hole in the middle. The code kills all clones (300 diamond shaped florets) but we have already "stamped" their image so we don't lose the pattern created by those first 300 clones. We then create new clones. The result is spirals with many more diamond florets than otherwise possible.) 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 See also our Scratch model using a pen rather than moving clones.
