It kind of isn’t. There are lots of *logarithmic* spirals in nature, but not all logarithmic spirals are Fibonacci spirals.
EDIT: this isn’t to say that Fibonacci numbers never turn up in nature. They are quite common in botany, for the patterns of seed growth in sunflower heads and pine cones, but it turns out that this is because logarithmic spirals with a rate of turn close to the golden ratio pack very efficiently. Also, the relationship between the Fibonacci numbers and the Golden Ratio is slightly deceptive. While the ratio between consecutive terms of the Fibonacci sequence does tend towards phi, this is not a particular property of that exact sequence, but is also true of all recursive sequences of the form
a, b, (a+b), ((a+b)+b)…
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