How to make a colour gradient with 60 lines on a graph

I have a program that puts 60 lines onto a singular graph. The 60 lines are the same equation being plotted with one variable changing for each iteration using a simple for loop. I was wondering if there was a way to make the lines change colours in a gradient so that the graph is easier to read by implementing a key. For example, as the value increases the colour would change gradually from yellow to orange to, finally, red. Here is the program for reference:

format long
 %DECLARE VARIABLES
M = 10000002;
w = zeros(M,1);
e = zeros(M,1);
dw = zeros(M-1,1);
de = zeros(M-1,1);
T = [0:10000000];
e(1) = 0.0549;
w(1) = 0.3844e9;
for g = 12.0:0.1:18.0
    
for m = 0:10000000
    de(m+1) = -(4e41 + (2.e40)/g) * ((w(m+1))^(-13/2)) * e(m+1);
    dw(m+1) = -((8.1e41)*(e(m+1)^2) + ((1.2e40)/g)) * (w(m+1))^(-11/2);
    
    e(m+2) = e(m+1) + (de(m+1) * 3.154e7);
    w(m+2) = w(m+1) + (dw(m+1) * 3.154e7);
end
e = e(1:end-1);
w = w(1:end-1);
plot (T, w)
hold on
end
hold off

Answer 1

[Voss]

You can set the ColorOrder property of the axes to control the colors of the plotted lines, without having to specify each line's color when it's plotted.

Something like this (here I've reduced the number of for loop iterations by a few orders of magnitude):

format long
 %DECLARE VARIABLES
M = 1002;%0002;
w = zeros(M,1);
e = zeros(M,1);
dw = zeros(M-1,1);
de = zeros(M-1,1);
T = [0:1000];%0000];
e(1) = 0.0549;
w(1) = 0.3844e9;


% set the axes ColorOrder:
cmap = flip(autumn(61),1); % yellow -> red, with 61 colors (for 61 lines)
set(gca(),'ColorOrder',cmap)
hold on


for g = 12.0:0.1:18.0
    
    for m = 0:1000%0000
        
        de(m+1) = -(4e41 + (2.e40)/g) * ((w(m+1))^(-13/2)) * e(m+1);
        dw(m+1) = -((8.1e41)*(e(m+1)^2) + ((1.2e40)/g)) * (w(m+1))^(-11/2);
        
        e(m+2) = e(m+1) + (de(m+1) * 3.154e7);
        w(m+2) = w(m+1) + (dw(m+1) * 3.154e7);
        
    end
    
    e = e(1:end-1);
    w = w(1:end-1);
    plot (T, w)
%     hold on
    
end

hold off

[AJ99]

This is very helpful thanks! Is there an easy way in MATLAB to also add a key?

[Voss]

You can easily add a colorbar that could serve as a key. Here I've done that, mapping yellow to 12 and red to 18, since those are the min and max values of g used for the lines (the colorbar is labelled as 'g' as well). You can change all of those things, of course.

format long
 %DECLARE VARIABLES
M = 1002;%0002;
w = zeros(M,1);
e = zeros(M,1);
dw = zeros(M-1,1);
de = zeros(M-1,1);
T = [0:1000];%0000];
e(1) = 0.0549;
w(1) = 0.3844e9;


% set the axes ColorOrder and ColorMap:
cmap = flip(autumn(61),1); % yellow -> red, with 61 colors (for 61 lines)
set(gca(), ...
    'ColorOrder',cmap, ...
    'ColorMap',cmap, ...
    'CLim',[12 18])
hold on
cb = colorbar();
cb.YLabel.String = 'g';


for g = 12.0:0.1:18.0
    
    for m = 0:1000%0000
        
        de(m+1) = -(4e41 + (2.e40)/g) * ((w(m+1))^(-13/2)) * e(m+1);
        dw(m+1) = -((8.1e41)*(e(m+1)^2) + ((1.2e40)/g)) * (w(m+1))^(-11/2);
        
        e(m+2) = e(m+1) + (de(m+1) * 3.154e7);
        w(m+2) = w(m+1) + (dw(m+1) * 3.154e7);
        
    end
    
    e = e(1:end-1);
    w = w(1:end-1);
    plot (T, w)
%     hold on
    
end

hold off

[AJ99]

This is incredibly useful thanks for the help again!

[Voss]

You're welcome!