Hello, for my final project in my computational physics class, I wanted to compare the Mandelbrot approximation of pi to Matlab's built in pi. I got the idea from a NumberPhile video: https://www.youtube.com/watch?v=d0vY0CKYhPY and here is my code so far:
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close all;clear all; clc %Prepared by Lauren Stearns
% Project: Using Matlab to evaluate pie via the Mandlebrot set and comparing the approximation to % Matlab's built in pi.
prompt = 'Input a small, real, positive value for epsilon. Input:';
c = 1/4 + input(prompt) ; % c needs to be greater than 1/4 such as 1/4 + epsilon. % Where epsilon is a very small, real, positive, number. 1/4 represents the
% cusp of the mandlebrot set.
z = 0; n = 0;
while z < 2 % The number of iterations required to surpass 2 is the approximation of pi.
z = z.^2 + c; n = n+1 ;
end
n format long
Pi = pi
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Table of Values obtained from running this code:
1) I wanted to know if there was a way to insert a period in front of the first digit in my n output. For example, I would like the n that corresponds to epsilon 1e-6 to be displayed as 3.1410 instead of 31410
2) My next question, is why won't anything to a higher power than epsilon = 1e-16 generate an output? 1e-16 gives me an out put (as seen in the table), but I let 1e-17 run for over 20 minutes and got nothing.
3) I also hoped to do a comparison at the end of my code between the output of n and Matlab's built in value for pi. I tried adding the following lines at the end of my code, but I couldn't figure out how to account for the changing magnitude of the iterations.
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Comparison = abs(((pi-n)/pi*10^(-4)))*100;
display(Comparison)
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4) Lastly, I noticed that only the even powers are converging to pi and the odd powers appear to be converging to 1. So why do only even powers converge to pi?
Any and all help would be greatly appreciated. Thank you for taking the time to read my post :)
