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.