% Here, I'm going to find out how 
% long it takes 3x+1 to get to 1.

% This is my threshold value, beyond 
% which I say "it never gets to 1."
threshold = 500;

% How many numbers should I try,
% and where should I start?
numstart = 1;
numend = 50000;
numsteps = zeros(1,numend);
avgsofar = zeros(1,numend);

for x=numstart:numend,

    count = 0;
    y = x;
    
    while y > 1 && count < threshold,
   
        % x is the start number. iterate, changing y!
        if mod(y,2)
            y = 3*y + 1;
        end
    
        y = y/2;
        count = count+1;
    
    end
    if y == 1
        % disp([num2str(x) ' went to 1 in ' num2str(count) ' steps.']);
    else
        disp(['**** ' num2str(x) ' did not go to 1!!! ****']);
    end
    numsteps(x) = count;
    avgsofar(x) = sum(numsteps) / x;
    
end

X = 1:length(numsteps);
Y = 6.95*log(X+1);
plot(X,numsteps,'.',X,avgsofar,'-',X,Y,'-');