I am trying to create a normal random moving point for each individual point in a 3D scatter point. How do I go about to do this?

I am trying to replicate the random movements (gaussian distribution) found in particles and to do that, I have already made a moving plot (in a normal random distribution) but I am trying to have a maybe 5 by 5 number of points with each point having its on random moving point.

Code attached are the moving plot and the scatter plot

[darova]

Can you be more specific? Here is the result of one of your script

How do you want it to look like?

[sui zhi lau]

Hi Darova,

Thanks for replying! For the moving plot, this would be counted as the movement for one 'particle'. So would it be possible for multiple points to be moving cocurrently in the same plot.

So for the no magnetic field code, I would like to have each point's arrow moving randomly. so it would be:

But with the same moving plot for each points on this plot.

Answer 1

[darova]

What about this?

n = 5;
[X,Y] = meshgrid(1:n);              % create mesh
T = 180*rand(n)-90;                 % initial angles
cla
plot(X(:),Y(:),'ob')                % plot starting points
hold on
for i = 1:30
    T = T + rand(n)*90 - 45;        % increase/decrease angle
    X = X + 0.05*cosd(T);           % increase/decrease X coordinate
    Y = Y + 0.05*sind(T);           % increase/decrease Y coordinate
    plot(X(:),Y(:),'.r')            % plot new coordinates
    pause(0.1)
end
hold off

[sui zhi lau]

Hi Darova,

Yes! This was what I kind of wanted but I am doing a project on particle 'jumps' so would it be possible for the moving dots to be arrows? And shouldn't the plots be jumping towards the centre after awhile due to it being a gaussian distribution?

Thanks so much for helping again.

Ash

[darova]

• would it be possible for the moving dots to be arrows?

Sure, do you know how quiver functoin works?

• And shouldn't the plots be jumping towards the centre after awhile due to it being a gaussian distribution?

Im bad at math. Can you show it on the picture? How should they move?

[sui zhi lau]

Yes I have been using the quiver function for my initial 2D moving plot.

So, the arrows should be moving in such a way that points should intercept alot back into the middle.

That is why the arrows in my moving plot 'jumps' back close to the centre.

So I am expecting my code to have my scatter plot to look something like this with individual random movement (if it is a 5 x 5 matrix):

[darova]

Was not that easy as i thought!

nmesh = 4;
niter = 40;
[X,Y] = meshgrid(0:nmesh-1); % create mesh
X = 5*X;
Y = 5*Y;
dx = normrnd(0,1,[nmesh^2 niter]);
dy = normrnd(0,1,[nmesh^2 niter]);
cla
plot(X(:),Y(:),'ob')         % plot starting points
hold on
plot(X,Y,'k')                % plot grid
plot(X',Y','k')
for i = 1:niter-1
    X1 = X(:) + dx(:,i);
    Y1 = Y(:) + dy(:,i);
    quiver(X1, Y1, dx(:,i+1)-dx(:,i), dy(:,i+1)-dy(:,i))
%     plot([X(:) X(:)]'+[dx(:,i+1) dx(:,i)]', ...
%          [Y(:) Y(:)]'+[dy(:,i+1) dy(:,i)]','.-r')
    pause(0.5)
end
hold off

[sui zhi lau]

Thank you so much Darova! That is the code that I want!

Just a side note:

Would it be possible if I change the distance between the 'particlles'. Because when I was changing:

X = 5*X;
Y = 5*Y;

into

X = 10*X;
Y = 10*Y;

It went out of sync with the particles' jumps

[darova]

It's because of quiver scale. If you uncomment this part

You will see the actual movement of your particles

Try to scale quiver

scale = 0.5;
quiver(X1, Y1, dx(:,i+1)-dx(:,i), dy(:,i+1)-dy(:,i),scale)

[sui zhi lau]

Oh sorry, I set the limit for the x and y coordinate. That was my mistake.

okay it works and I am happy with the answer you gave me!

But if possible, if I wanted to put it into a 3D format, what would I need to change/add?

[darova]

You mean like this? Z coordinate?

[sui zhi lau]

Nope ! more like the previous codes but rather than the arrows moving in 2 directions, they are moving in a 3 dimensional area in like a for example 5 by 5 by 5 particles.

So still something like this but the arrows are moving in 3 directions (x,y and z coordinates)

[darova]

What if just add

dz = normrnd(0,1,[nmesh^2 niter]);
%
Z1 = 0 + dz(:,i);

And use quiver3?

[sui zhi lau]

Yes I tried that but it kept showing errors

nmesh = 5;
niter = 40;
scale = 0.5;
[X,Y,Z] = meshgrid(0:nmesh-1); % create mesh
X = 5*X;
Y = 5*Y;
Z = 5*Z;
dx = normrnd(0,1,[nmesh^2 niter]);
dy = normrnd(0,1,[nmesh^2 niter]);
dz = normrnd(0,1,[nmesh^2 niter]);
cla
plot3(X(:),Y(:),Z(:),'ob')         % plot starting points
hold on
%plot(X,Y,'k')                % plot grid
%plot(X',Y','k')
for i = 1:niter-1
    X1 = X(:) + dx(:,i);
    Y1 = Y(:) + dy(:,i);
    Z1 = 0 + dz(:,i);
    quiver3(X1, Y1, Z1, dx(:,i+1)-dx(:,i), dy(:,i+1)-dy(:,i),dz(:,i+1)-dz(:,i))
     %plot([X(:) X(:)]'+[dx(:,i+1) dx(:,i)]', ...
         %[Y(:) Y(:)]'+[dy(:,i+1) dy(:,i)]','.-r')
    pause(0.5)
end
hold off
rotate3d on

[darova]

Try this modifications

[sui zhi lau]

hi darova,

This is a long shot but would it be posisble to add certain range of values to converge to the centre of the plot but it does not show any changes.

I have attached my code and a rough guide as to how I would like my point to converge to the centre with arrows.

I would like the points at the red box to change from random moving points to points moving towards the centre (black box)

I have attached my MATLAB file and hope that my explanation of my problem makes sense.

clc;    % Clear the command window.
close all;  % Close all figures (except those of imtool.)
clear;  % Erase all existing variables. Or clearvars if you want.
workspace;  % Make sure the workspace panel is showing.
%%
scale = 0.5;
k = -1;
y = 1;
nmesh = 5;
niter = 40; %no. of jumps
s = 35.3;% size of particle -> diameter = 45 nm , area of circle = 35.343 nm^2 

[X,Y] = meshgrid((-nmesh+1):nmesh-1); % create mesh of -X -> X, -Y -> Y

X = 10*X;
Y = 10*Y;
dx = normrnd(0,1,[(size(X,1))^2 niter]); %
dy = normrnd(0,1,[(size(X,1))^2 niter]);
MagF=X/2;
countmax = size(X,1);
cla
%plot(X(:),Y(:),'ob')% plot starting points
%%
grid off
hold on
%plot(X,Y,'k')                % plot grid
%plot(X',Y','k')
%%
for i = 1:niter-1
    X1 = X(:) + dx(:,i);
    Y1 = Y(:) + dy(:,i);
    if (-MagF < X < MagF) 
            %U = X - X;
            %V = Y - Y;
         U = k.* ones(1,length(X))
         V = zeros(1,countmax)
        u = U;
        v = V;
        u(1:(countmax-1))=0
        v(1:(countmax-1))=0
        q1 = quiver(X1,Y1,u,v)
        q1.LineWidth = s;
        hold on
        grid on
        %%
        else
   % q = quiver(X1, Y1, (dx(:,i+1)-dx(:,i))*1.1, 1.1*(dy(:,i+1)-dy(:,i)),scale)
    q.ShowArrowHead = 'off';
    q.LineWidth = 3;
%     plot([X(:) X(:)]'+[dx(:,i+1) dx(:,i)]', ...
%          [Y(:) Y(:)]'+[dy(:,i+1) dy(:,i)]','.-r')
    pause(0.5)
    %% percentage readings  
    Image = getframe();
    K = sum(sum(rgb2gray(Image.cdata)==255));                                 
    percentageofwhite(y) = K/numel(rgb2gray(Image.cdata))*100;
    delete(findall(gcf,'type','text'))
    txt=text(0.0,0.95,sprintf('White Space = %0.3f%%',percentageofwhite(y)),'Units','normalized');
    y=y+1;
    xlim([-nmesh^2 nmesh^2])
    ylim([-nmesh^2 nmesh^2])
    end
end
hold off

[darova]

Is it possible for you to make a simple sketch like this?

How do you imagine your result to look

[sui zhi lau]

So if possible, set a range to show how far the magnetic strength (for the above picture, it is x<=30 && y<=30) and each particle will move towards the centre incrementally (small jumps towards the centre) while the rest jumps randomly as usual.

[darova]

Try this

c0 = nmesh;                         % center of magnetic field
for i = 1:size(dx,1)
    [ii,jj] = ind2sub(size(X),i);   % row and column of force
    n = hypot(ii-c0,jj-c0);         % distance to point
    if n < 2.1                      % radius of magnetic force
        dx(i,:) = -cumsum(dx(i,:)*0+(jj-c0)/n);  % cosinus
        dy(i,:) = -cumsum(dy(i,:)*0+(ii-c0)/n);  % sinus
    end
end

[sui zhi lau]

Sorry but how am i supposed to put this in ?

clc;    % Clear the command window.
close all;  % Close all figures (except those of imtool.)
clear;  % Erase all existing variables. Or clearvars if you want.
workspace;  % Make sure the workspace panel is showing.
%%
scale = 0.5;
y = 1;
nmesh = 8;
niter = 40;
[X,Y] = meshgrid(0:nmesh-1) % create mesh
X = 10*X;
Y = 10*Y;
dx = normrnd(0,1,[nmesh^2 niter]);
dy = normrnd(0,1,[nmesh^2 niter]);

cla
%plot(X(:),Y(:),'ob')% plot starting points
%%
grid off
hold on
%plot(X,Y,'k')                % plot grid
%plot(X',Y','k')
%%
for i = 1:niter-1
    X1 = X(:) + dx(:,i);
    Y1 = Y(:) + dy(:,i);
    q = quiver(X1, Y1, (dx(:,i+1)-dx(:,i)), (dy(:,i+1)-dy(:,i)),scale)
    q.ShowArrowHead = 'on'
    q.LineWidth = 3
%     plot([X(:) X(:)]'+[dx(:,i+1) dx(:,i)]', ...
%          [Y(:) Y(:)]'+[dy(:,i+1) dy(:,i)]','.-r')
    pause(0.5)
    %% percentage readings  
    Image = getframe();
    K = sum(sum(rgb2gray(Image.cdata)==255));                                 
    percentageofwhite(y) = K/numel(rgb2gray(Image.cdata))*100;
    delete(findall(gcf,'type','text'))
    txt=text(0.0,0.95,sprintf('White Space = %0.3f%%',percentageofwhite(y)),'Units','normalized');
    y=y+1;
    xlim([-nmesh nmesh^2])
    ylim([-nmesh nmesh^2])
end
hold off

[darova]

After defining dx dy

[sui zhi lau]

ya i define but i am still getting only the random moving ones ?

clc;    % Clear the command window.
close all;  % Close all figures (except those of imtool.)
clear;  % Erase all existing variables. Or clearvars if you want.
workspace;  % Make sure the workspace panel is showing.
%%
scale = 0.5;
y = 1;
nmesh = 8;
niter = 40;
[X,Y] = meshgrid(0:nmesh-1) % create mesh
X = 10*X;
Y = 10*Y;
dx = normrnd(0,1,[nmesh^2 niter]);
dy = normrnd(0,1,[nmesh^2 niter]);

cla
%plot(X(:),Y(:),'ob')% plot starting points
%%
grid off
hold on
%plot(X,Y,'k')                % plot grid
%plot(X',Y','k')
%%
c0 = nmesh;                         % center of magnetic field
for i = 1:size(dx,1)
    [ii,jj] = ind2sub(size(X),i);   % row and column of force
    n = hypot(ii-c0,jj-c0);         % distance to point
    if n < 2.1                      % radius of magnetic force
        dx(i,:) = -cumsum(dx(i,:)*0+(jj-c0)/n);  % cosinus
        dy(i,:) = -cumsum(dy(i,:)*0+(ii-c0)/n);  % sinus
    end
        plot([X(:) X(:)]'+[dx(:,i+1) dx(:,i)]', ...
        [Y(:) Y(:)]'+[dy(:,i+1) dy(:,i)]','.-r')
    %% percentage readings  
    Image = getframe();
    K = sum(sum(rgb2gray(Image.cdata)==255));                                 
    percentageofwhite(y) = K/numel(rgb2gray(Image.cdata))*100;
    delete(findall(gcf,'type','text'))
    txt=text(0.0,0.95,sprintf('White Space = %0.3f%%',percentageofwhite(y)),'Units','normalized');
    y=y+1;
    xlim([-nmesh nmesh^2])
    ylim([-nmesh nmesh^2])
end
hold off

[darova]

Are you kidding with me?

[sui zhi lau]

Im sorry Darova if i asked something ignorant. I only picked up MATLAB just late last year and I am still getting confused since most of what i did are self-learned.

Anyways, if possible, would you mind vetting through my 3D plot? I tried to change it up but I cant get it to run

Sorry for the trouble

clc;        % Clear the command window.
close all;  % Close all figures (except those of imtool.)
clear;      % Erase all existing variables. Or clearvars if you want.
workspace;  % Make sure the workspace panel is showing.
niter = 40; % no. of jumps
scale = 0.5; 
y = 1; % white percentage
%% range of results
d = 1;
nmesh = 4; %range 
[X,Y,Z] = meshgrid((-nmesh+1):nmesh-1); % create mesh
X = X * d;
Y = Y * d;
Z = Z * d;
%% random direction for X,Y,Z
dx = normrnd(0,1,[(size(X,1))^3 niter]);
dy = normrnd(0,1,[(size(X,1))^3 niter]);
dz = normrnd(0,1,[(size(X,1))^3 niter]);
%% Magnetised particles
c0 = nmesh;                         % center of magnetic field
for i = 1:size(dx,1)
    [ii,jj] = ind2sub(size(X),i);   % row and column of force
    n = hypot(ii-c0,jj-c0);         % distance to point
    if n < 3.5                      % radius of magnetic force
        dx(i,:) = -cumsum(dx(i,:)*0+(jj-c0)/n);  % cosinus
        dy(i,:) = -cumsum(dy(i,:)*0+(ii-c0)/n);  % sinus
        dz(i,:) = -cumsum(dz(i,:)*0+(ii-c0)/n);
    end
end
cla
%plot3(X(:),Y(:),Z(:),'ob')         % plot starting points
hold on
%plot(X,Y,'k')                % plot grid
%plot(X',Y','k')
%% For Loop to plot graph
for i = 1:niter-1
    X1 = X(:) + dx(:,i);
    Y1 = Y(:) + dy(:,i);
    Z1 = Z(:) + dz(:,i);
    %q = quiver3(X1, Y1, Z1, dx(:,i+1)-dx(:,i), dy(:,i+1)-dy(:,i),dz(:,i+1)-dz(:,i))
    %q.LineWidth = s;
    %q.ShowArrowHead = 'off';
     plot3([X(:) X(:)]'+[dx(:,i+1) dx(:,i)]', ...
         [Y(:) Y(:)]'+[dy(:,i+1) dy(:,i)]',...
         [Z(:) Z(:)]'+[dz(:,i+1) dz(:,i)]','.-r')
    pause(0.05)
    %% percentage readings  
    Image = getframe();
    K = sum(sum(rgb2gray(Image.cdata)==255));                                 
    percentageofwhite(y) = K/numel(rgb2gray(Image.cdata))*100;
    delete(findall(gcf,'type','text'))
    txt=text(0.0,0.95,sprintf('White Space = %0.3f%%',percentageofwhite(y)),'Units','normalized');
    y=y+1;
    xlim([-5*d d*5])
    ylim([-5*d d*5])
end
hold off
xlabel('My x label')
ylabel('My y label')
zlabel('My z label')
rotate3d on

[darova]

Try this

Why the code is not color? Is it because you are sad?

[sui zhi lau]

I tried it and it showed this

I dont see the random movements or the coverging to the centre.

clc;    % Clear the command window.
close all;  % Close all figures (except those of imtool.)
clear;  % Erase all existing variables. Or clearvars if you want.
workspace;  % Make sure the workspace panel is showing.
niter = 40; % no. of jumps
scale = 0.5; 
y = 1; % white percentage
%% range of results
d = 1;
nmesh = 4; %range 
[X,Y,Z] = meshgrid((-nmesh+1):nmesh-1); % create mesh
X = X * d;
Y = Y * d;
Z = Z * d;
%% random direction for X,Y,Z
dx = normrnd(0,1,[(size(X,1))^3 niter]);
dy = normrnd(0,1,[(size(X,1))^3 niter]);
dz = normrnd(0,1,[(size(X,1))^3 niter]);
%% Magnetised particles
c0 = nmesh;                         % center of magnetic field
for i = 1:size(dx,1)
    [ii,jj,kk] = ind2sub(size(X),i);   % row and column of force
    n = pdist2([ii jj kk],[c0 c0 c0]);         % distance to point
    if n < 2.1                      % radius of magnetic force
        dx(i,:) = -cumsum(dx(i,:)*0+(ii-c0)/n);  % cosinus
        dy(i,:) = -cumsum(dy(i,:)*0+(jj-c0)/n);  % sinus
        dz(i,:) = -cumsum(dz(i,:)*0+(kk-c0)/n);
    end
end
cla
%plot3(X(:),Y(:),Z(:),'ob')         % plot starting points
hold on
%plot(X,Y,'k')                % plot grid
%plot(X',Y','k')
%% For Loop to plot graph
for i = 1:niter-1
    X1 = X(:) + dx(:,i);
    Y1 = Y(:) + dy(:,i);
    Z1 = Z(:) + dz(:,i);
    %q = quiver3(X1, Y1, Z1, dx(:,i+1)-dx(:,i), dy(:,i+1)-dy(:,i),dz(:,i+1)-dz(:,i))
    %q.LineWidth = s;
    %q.ShowArrowHead = 'off';
     plot3([X(:) X(:)]'+[dx(:,i+1) dx(:,i)]', ...
         [Y(:) Y(:)]'+[dy(:,i+1) dy(:,i)]',...
         [Z(:) Z(:)]'+[dz(:,i+1) dz(:,i)]','.-r')
    pause(0.001)
    %% percentage readings  
    Image = getframe();
    K = sum(sum(rgb2gray(Image.cdata)==255));                                 
    percentageofwhite(y) = K/numel(rgb2gray(Image.cdata))*100;
    delete(findall(gcf,'type','text'))
    txt=text(0.0,0.95,sprintf('White Space = %0.3f%%',percentageofwhite(y)),'Units','normalized');
    y=y+1;
    xlim([-5*d d*5])
    ylim([-5*d d*5])
end
hold off
xlabel('My x label')
ylabel('My y label')
zlabel('My z label')
rotate3d on

[darova]

Please see this