Creating a 3D plot in Matlab

Question

I want to create a 3D plot of the final fraction of grass covered on the Earth (=in 2 billion years from now) (=A) as a function of a varying death rate of grass (=D) and the growth rate of grass (=G).

The final value of A (at 2 billion years away from now) can be calculated using a loop with the following discritised equation:

A(t+dt) = A(t)*((1-A(t))*GD)*dt + A(t)

%Define variables and arrays

D=0.1;                              %constant value 
G=0.4;                              %constant value
A=0.001;                            %initial value of A at t=0
t=0;
dt=10E6; 
startloop=1;                        %define number of iterations
endloop=200;                  

timevector=zeros(1,endloop);        %create vector with 0
grassvector=zeros(1,endloop);

%Define the loop

for t=startloop:endloop
    A=A.*((((1-A).*G)-D)) + A;   
    grassvector(t)=A;
    timevector(t)=t*dt;
end

Now i'm stuck on how to create a 3D plot of this final value of A as a function of a varying G and D. I got this but after a few trials, it keeps giving errors:

%(1) Create array of values for G and D varying between 0 and 1

A=0.001;
G=[0.005:0.005:1];           %Vary from 0.005 to 1 in steps of 0.005
D=[0.005:0.005:1];           %Vary from 0.005 to 1 in steps of 0.005

%(2) Meshgrid both variables = all possible combinations in a matrix

[Ggrid,Dgrid]=meshgrid(G,D);

%(3) Calculate the final grass fraction with varying G and D

D=0.1;
G=0.4;
A=0.001;
t=0;
dt=10E6; 
startloop=1;                        %define number of iterations
endloop=200;                  

timevector=zeros(1,endloop);        %create vector with 0
grassvector=zeros(1,endloop);

%Define the loop

for t=startloop:endloop
    A=A.*((((1-A).*Ggrid)-Dgrid)) + A;   
    grassvector(t)=A;
    timevector(t)=t*dt;
end

%(4) mesh together with D and G
...??

Can someone help? Thanks!

Answer 1

Your code is wrong, as grassvector(t)=A; can not be executed, as the sizes are not consistent. However, I think you may want to do:

grassvector=zeros([size(Ggrid),endloop]);

and in the loop:

grassvector(:,:,t)=A;

Also, while completely unnecesary computationally, you may want to initialize A to A=0.001*ones(size(Dgrid)) , as it makes more sense logically.

Anyways: this is how you can plot it in the end:

surf(Ggrid,Dgrid,A,'LineStyle','none');
xlabel('growth rate ')
ylabel('death rate ')
zlabel('grass')
colorbar

gives:

But, as I was actually interested in your research, I decided to make a couple of plots to see how fast the grass will grow and stuff. Here is some nice plotting code. You can modify different stuff here to be able to change the appearance of it. I use custom colormaps, so if it doesn't work, delete the colormap(viridis()) line. If you like the colormap, visit this .

fh=figure();
filename='grass.gif';
for t=startloop:endloop
    clf
    hold on
    surf(Ggrid,Dgrid,grassvector(:,:,t),'LineStyle','none');
    [c,h]=contour3(Ggrid,Dgrid,grassvector(:,:,t)+0.05,[0:0.1:1],'LineColor',[153,0,18]/255,'LineWidth',2);
    clabel(c,h);
    xlabel('growth rate ')
    ylabel('death rate ')
    zlabel('grass')
    title(['Years passed: ' num2str(t*dt/1000000) ' million'])
    colormap(viridis())
    axis([0 1 0 1 0 1])
grid on
    view(-120,40);

    frame = getframe(fh);
    im = frame2im(frame);
    [imind,cm] = rgb2ind(im,256);
    if t == 1;
        imwrite(imind,cm,filename,'gif', 'Loopcount',inf);
    else
        imwrite(imind,cm,filename,'gif','WriteMode','append','DelayTime',0.1);
    end
end

Results: