How to plot the number of iterations as a function of the approximation

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Lauren Stearns 2017-6-6

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/343472-how-to-plot-the-number-of-iterations-as-a-function-of-the-approximation

评论： Lauren Stearns 2017-6-6

Hello, My code provides me with an approximation of pi based on the number of iterations required to escape the Mandelbrot set. I would like to plot the number of iterations (n) as a function of the Approximation, but I can't seem to get a decent graph. I have tried just plotting n,Approximations, as well as a loglog plot (since the iterations get rather large) and I tried changing the marker size encase it was too small. I also tried to create a new loop to save the value from each iteration in a zeros matrix and plot that, but didn't really get anywhere with it. Any thoughts or ideas would be most appreciated. Here is the code:

% Fifth Version
close all;clear all; clc
%Prepared by Lauren Stearns
prompt = 'Input a small, real, positive value for epsilon.  Input:';
epsilon = str2double(input(prompt,'s')); 
c = 1/4 + epsilon ;  
% Where epsilon is a very small, real, positive, number. such as 1e-10
z = 0;
n = 0;
while z < 2
z = z.^2 + c;
n = n+1 ;
end
Approximation = n*sqrt(epsilon);
display(Approximation)
format long
Pi = pi
Comparison = abs(((pi-Approximation)/pi))*100;  %%Percent error comparison
display(Comparison)
loglog(n,Approximation,'k-', 'markersize', 12)

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Answer 1

KSSV 2017-6-6

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/343472-how-to-plot-the-number-of-iterations-as-a-function-of-the-approximation#answer_269691

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I literally, have no idea on what you are doing..but this can be done to plot number of iterations and approximation. You have to rethink on what you are doing:

close all;clear all; clc
%Prepared by Lauren Stearns
prompt = 'Input a small, real, positive value for epsilon.  Input:';
epsilon = str2double(input(prompt,'s'));
c = 1/4 + epsilon ;
% Where epsilon is a very small, real, positive, number. such as 1e-10
z = 0;
n = 0;
while z < 2
    z = z.^2 + c;
    n = n+1 ;
end
Approximation = [1:n]*sqrt(epsilon);
% display(Approximation)
format long
Comparison = abs(((pi-Approximation)/pi))*100;  %%Percent error comparison
% display(Comparison)
loglog(1:n,Approximation,'k-', 'markersize', 12)