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Plants, continued fractions, and the golden ratio | benkuhn.net

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where should one grow one’s leaves? • sunlight maximization • the most irrational number • Fibonacci phyllotaxis

You are a plant. You have a stem, and you can sprout off leaves from the stem in various directions. You want to maximize the amount of sunlight that hits your leaves, i.e., you want the angular distance between your leaves to be as wide as possible. However, as a plant, you aren't very smart. You can only grow in patterns with a constant angle between any two successive leaves-so if your first leaf points north and your second points east, the third one must point south and the fourth one west. 1 You may be a dumb plant, but you have been fine-tuned by evolution for hundreds of millions of ye

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