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Fibonacci number has something to do with natural growth. Though the function is very straight forward, we see this in nature. Does nature follow the function or its the simplified model of the function that nature follows?

Where do we see Fibonacci number? In flower petals, tree branches etc.

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    Phyllotaxis is extensively discussed in the literature. A very readable account occurs in Chapter 4 of the 2010 book by Ian Stewart, _The Mathematics of Life_. Indeed, many other solutions of the _generalised_ Fibonacci numbers are observed in nature.2011-12-21

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I read in the comments: It seems to be false claim. This is far from being consensual. You have many publications claiming that this is true, including very recent ones, eg this one: The phyllotaxis of the model plant Arabidopsis thaliana follows a Fibonacci spiral, the most frequent phyllotactic pattern found in nature.

Many publications propose models to explain this phenomenon, eg this one (published in 2011).

This book chapter by S Douady who wrote several papers on the subject might interest you (the last page is missing but all the models are fully described).

PS: Nice video with lots of examples, no explaination or modeling.