MATLAB Matlab field (quiver) plot and gradient

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The discussion centers around an issue with the Matlab quiver plot, specifically regarding the computation of the gradient vector when using an exponential function as a velocity field. The user shares a code snippet that demonstrates how the velocity field is generated based on specified datapoints, which represent charges. The gradient is calculated using the `gradient` function, and the quiver plot is intended to visualize the resulting vector field. A key point raised is the indexing scheme used in Matlab, where the field is indexed as `field(y,x)`, which may lead to confusion when interpreting the output. The user emphasizes that understanding this indexing is crucial for accurately representing the velocity field in the quiver plot.
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I have been playing around with the Matlab quiver plot, and I found something strange: it seems that the gradient vector isn't computed correctly. ( I use the gradient of an exponential function as a velocity field). Please try the following code. The interesting part is in the last loop (simtime). (It's in the attachment as well.)

Code: 
clear;
hold on
figure(1);
title_handle = title('cucc');
simtime = 100;
lenx=50;
leny=50;
field = zeros(lenx,leny);
%field = randn(lenx,leny);


d.x = 20;
d.y = 20;
d.width = 20;
d.height = 10;
datapoints(1) = d;
% these will be the charges, or whatever 

%{
d.x = 30;
d.y = 10;
d.width = 6;
d.height = 3;
datapoints(2) = d;

d.x = 40;
d.y = 25;
d.width = 2;
d.height = 3;
datapoints(3) = d;
%}

for i=1:lenx,
    for j=1:leny,        
        dp = datapoints;      
        for k=1:length(dp),
            field(i,j) = field(i,j) + exp(-1*((dp(k).x-i)^2+(dp(k).y-j)^2)/dp(k).width^2)*dp(k).height;
        end        
    end
end

[DX,DY] = gradient(field,1,1);
quiver(DX,DY);

hold on 

rect.x=3;
rect.y=37;
fill([rect.x,(rect.x+1),(rect.x+1),rect.x],[rect.y,rect.y,(rect.y+1),(rect.y+1)],'g');
ht=fill([rect.x,(rect.x+1),(rect.x+1),rect.x],[rect.y,rect.y,(rect.y+1),(rect.y+1)],'r');
for i=1:simtime,
    ix=(round(rect.x));
    iy=(round(rect.y));
    dx = DX(ix,iy)
    dy = DY(ix,iy)
    rect.x = dx+rect.x;
    rect.y = dy+rect.y;
    X=[rect.x,(rect.x+1),(rect.x+1),rect.x];
    Y=[rect.y,rect.y,(rect.y+1),(rect.y+1)];
    set(ht,'XData',X); % redrawing the moving square
    set(ht,'YData',Y);
        
    str1 = num2str((round(rect.x)),'x:%d, ');
    str2 = num2str((round(rect.y)),'y:%d ');
    str = strcat(str1,str2)

    set(title_handle,'String',str);
    drawnow
end
hold off
 

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Now I've got it.
Both the gradient func., both quiver plot uses the following indexing scheme:
field(y,x)