Fibonacci spirals

Fibonacci spirals can be found everywhere in nature from sunflower seed heads to pine cone scales, succulent leaves, cacti spines and many many more.

 Fibonacci spirals spotted at Kew Gardens

Fibonacci spirals spotted at Kew Gardens

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The Fibonacci spiral is an approximation of the golden spiral created by drawing circular arcs connecting the opposite corners of squares in the Fibonacci tiling; this one uses squares of sizes 1, 1, 2, 3, 5, 8, 13 and 21.
— John Hudson Tiner (200). Exploring the World of Mathematics: From Ancient Record Keeping to the Latest Advances in Computers

 

This video illustrates it beautifully. Take a few minutes out of your day to watch it - you won't regret it!

Here are a few pictures from my archives of illustrations showing fibonacci spirals.

 Sequoia cone

Sequoia cone

 Another pine cone

Another pine cone

 Cycad trunk

Cycad trunk

 Cactus spines

Cactus spines