Collatz Sequence Plotting Issue

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?

[Walter Roberson]

What would be on the y axis again? The sequence length n(i) for position i? Or the maximum sequence length over 1:n(i) for position i?

[Reelz]

the y- axis would be the values of x (the integer values for the steps) and on x-axis would be the so called 'i' values, for i = 0, 1,2....etc.

I'm just not sure how to plot these values from my second code.

[Walter Roberson]

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]

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)

Answer 1

[Thomas]

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)

[Reelz]

I already did that, I am trying to plot different values if you read above

[Thomas]

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..?