Published on Sep 28, 2024
The objective: The purpose of this project is to see if the nth root of the absolute value of the nth term in a random Fibonacci sequence approaches v (1.1319...). The project also resolves a discrepancy between two different published descriptions of the random Fibonacci sequence. The hypothesis of this project is that the nth root does approach v and the original description of the behavior of the random Fibonacci sequence, by Divakar Viswanath, is more correct.
The hypothesis is tested by generating a random Fibonacci sequence and determining the nth root of it to see if it converges on v. This experiment will also test to see if Mario Livio is right about the random Fibonacci sequence converging at around the hundredth number in the sequence.
To simulate this, the experiment uses a Visual Basic computer program with a pseudo random number generator to choose the operators. An order to perform this experiment the computer needs Microsoft Visual Basic installed into Excel.
The results show that the nth root of the nth term does eventually approach v, but very far into the sequence. Although the results vary because of the randomness of the sequence, the nth root typically becomes very close to v when n is approximately equal to 50,000.
The nth root of the nth term approaches v well past the hundredth number in the sequence. This supports Viswanaths conclusions on random Fibonacci sequences.
This Mathematical project explores and tests the behaviors of a random Fibonacci sequence, a variant of the Fibonacci sequence.