Plotting Matrix Columns with Colorbar

I have an array that is long in one dimension and short in another, let's say 50 x 5000. Each of the 50 rows is a point in space and each of the 5000 columns is a time. I would like to plot isochrones as so:

X = 50;
T = 5000;
x = 0:X;
t = 0:T;
M = somefun(x,t);
plot(M(:,1234),x);

However, I would like to plot many irregularly- (logarithmically?) spaced columns and would like to color them with increasing time and provide a corresponding colorbar. I can think of several ways to brute-force this, but I suspect that there is a simple way that I am missing.

Any help will be greatly appreciated.

[Walter Roberson]

T Matthew Evans commented,

I posted this question under an alias that I do not really use. I have reformulated the question in a somewhat more complete way and re-posted under my preferred alias. I would like very much to delete this question, please. Thank you.

[Walter Roberson]

T Matthew Evans:

Our policy is that questions that have received a meaningful volunteer attempt at an answer are not deleted or closed, not unless the question is abusive or not permitted by law. This policy is in place to respect the efforts of the volunteers.

You can post a link to the updated question.

Answer 1

[KSSV]

How about this approach?

x = 0:.05:2*pi;
y = sin(x);
z = zeros(size(x));
col = x;  % This is the color, vary with x in this case.
surf([x;x],[y;y],[z;z],[col;col],...
        'facecol','no',...
        'edgecol','interp',...
        'linew',5);
colorbar

[Moe Szyslak]

Thanks for the response, but I am not sure this is exactly what I want. I'd like to have each column of the array plotted as a different color corresponding to a colorbar of (essentially) increasing column index. Maybe I need to build my array in a different way?

[KSSV]

Give same value for each column and use surf.

[Moe Szyslak]

I'm not sure surf will get me what I want -- here's a cartoon of what I am looking for. Does this make sense?