Collatz Sequence Plotting Issue

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Reelz
Reelz 2012-4-22
I have written code for the collatz problem, and performed some plotting for the number of steps versus the integer values. But now I am trying to plot the values of i versus my xi values *for i = 1 : 300.
Here is my code:
function [ns, seq] = collatz(n)
% first number insequence is n
seq(1) = n;
% position an index on the next element of sequence
i = 2;
% Repeat until you find a 1
while seq(i-1) ~= 1
% mod after division to find an even/odd number
if mod(seq(i-1), 2) == 0
% Step if even
seq(i) = seq(i-1)/2;
else
% Step taken if odd
seq(i) = 3*seq(i-1) + 1;
end
% index increment
i = i+1;
end
% Find length of the sequence
ns = length(seq);
Running Program:
>> [n, seq] = collatz(300)
n =
17
seq =
300 150 75 226 113 340 170 85 256 128 64 32 16 8 4 2 1
Then I wrote this code for the max values of xi with the largest number of steps for i = 1 : 300.
% For max number of steps for i = 1 : 300
clc; clear
% Sequence for max steps for
for i = 1 : 300
% Perform the function and get the number of elements
[n(i), seq{i}] = collatz(i);
end
% Find max number of steps found
[max_steps, ix] = max(n)
% Display the appropriate indexed sequence
seq{ix}
% Running Function:
max_steps =
128
ix =
231
How would I plot i on the x-axis versus my values of xi on the y - axis?
  4 个评论
显示 2更早的评论
Walter Roberson
Walter Roberson 2012-4-23
Please clarify. There is no "x" variable in your code. You have an "ix" variable, but that is obtained as the position the maximum length occurs over i=1:n and is thus a one-time thing not something that can be plotted against "i". Unless, that is, you want to modify the code slightly so that "ix" are the index of the "running maximum" -- e.g., if at "i" = 58 the maximum so-far had been at "i = 43" then ix(58) would be 43 ??
Reelz
Reelz 2012-4-23
Exactly, this largest value of (not ix, sorry I meant xsubi) xi(58) which is 43 would be what I want to plot. So using your example I would take this 43 (since it has the largest number of steps u to 58) and make a graph with the values of i on the x-axis, and the values of ix on the y-axis. (looking at my first code may make it make more sense)

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回答（1 个）

Thomas
Thomas 2012-4-23
You could plot the number of steps required to get to 1 as shown in the Wolfram mathworld link
http://mathworld.wolfram.com/CollatzProblem.html
You could do it simply by
plot(n,'MarkerSize',10,'Marker','.','LineStyle','none');
% Create xlabel
xlabel('Number');
% Create ylabel
ylabel('Steps to reach 1');
EDIT If the largest upto a number is needed
for i=1:300
newmax(i)=max(n(1:i))
end
plot(newmax)
  2 个评论
Reelz
Reelz 2012-4-23
I already did that, I am trying to plot different values if you read above
Thomas
Thomas 2012-4-23
R you trying to see what the largest value at each of the numbers from 1:300 are i.e. if n=1 2 8 3 6 9 17
at 1 Largest =1
2, largest=2
3, largest =8
4,largest =8
5,largest=8
6 largest=9 and so on..?

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