I was just wondering what were the main/important uses of the Fibonacci sequence as well as any other generalized Fibonacci sequences in real life applications.
As far as I know, the Fibonacci sequence have no particular "uses" in real life and they are more relevant in the frame of certain mathematical models.
A particular application I think of is when you know that a function has a single maximum in a given interval. Then it is proven that the optimal sequence of function evaluations to narrow down the maximum is obtained with intervals having a length proportional to the terms of Fibonacci.
But I wouldn't call that real life.
In computer science, there is a data structure called a Fibonacci Heap that works by storing items in a collection of heaps with degrees that are ascending Fibonacci numbers. Fibonacci heaps have significantly better performance in certain tasks than other similar data structures.
The number of ways you can climb stairs from 0 to stair N is a fibonacci sequence provided you can climb 1 or 2 stairs at one time. Not real life really but if you want to know :D