Choose number of colors and click flag. Altering number of colors highlights different spiral patterns. Hit space key to freeze. Each new floret turns 137.5 degrees, the angle that best fills the space. Count the numer of clockwise spirals and count the counterclockwise spirals. Each will be a Fibonacci number. Each new floret shows it's birth order, 1, 2,3... If you subtract successive numbers in a spiral you will find Fibonacci numbers (such as 13, 21, 34, 55, 89...). Hit "h" key to hide number of colors slider.
Sunflower painting by Kathy, using spiral I generated with Scratch. 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. Uses 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. Had to make costumes for numbers, but only made costumes for up to 102 numbers. After that number, the cycle repeats. (the code kills 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 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.
