The Math of Nature’s Design: From Fibonacci Spirals to Recursive Games
The Fibonacci sequence—defined by the recurrence F(n) = F(n−1) + F(n−2) with F(0)=0 and F(1)=1—holds a unique place in mathematics and natural design. This simple rule, starting with 0 and 1, cascades into a pattern where each number is the sum of the two preceding: 0, 1, 1, 2, 3, 5, 8, 13, 21…
These numbers mirror nature’s tendency toward efficient growth and self-similarity.
The Golden Spiral: A Blueprint in Sunflowers and ShellsOne of the most striking manifestations of Fibonacci numbers is the golden spiral, observed in sunflower seed heads, pinecones, and nautilus shells. As seeds or scales are arranged along phyllotactic angles—approximately 137.5°, the golden angle—spirals emerge in clockwise and counterclockwise directions.