How do I make a 2D randomwalk?

I have so far only been able to make a 1D randomwalk but I have to make it into 2D. Below is my code for 1D. How do I change it so that it is in 2D?

 clear
 clc

 N = 100; % Length of the x-axis, also known as the length of the random walks.
 M = 400; % The amount of random walks.
 x_t(1) = 0;

 for m=1:M
    for n = 1:N % Looping all values of N into x_t(n).
        A = sign(randn); % Generates either +1/-1 depending on the SIGN of RAND.
        x_t(n+1) = x_t(n) + A;
    end
    plot(x_t);
    hold on
 end

Answer 1

[Image Analyst]

Just duplicate everything for y:

clc;
clearvars;

N = 100; % Length of the x-axis, also known as the length of the random walks.
M = 400; % The amount of random walks.
x_t(1) = 0;
y_t(1) = 0;

for m=1:M
  for n = 1:N % Looping all values of N into x_t(n).
    A = sign(randn); % Generates either +1/-1 depending on the SIGN of RAND.
    x_t(n+1) = x_t(n) + A;
    A = sign(randn); % Generates either +1/-1 depending on the SIGN of RAND.
    y_t(n+1) = y_t(n) + A;
  end
  plot(x_t, y_t);
  hold on
end
grid on;
% Enlarge figure to full screen.
set(gcf, 'Units', 'Normalized', 'Outerposition', [0, 0.05, 1, 0.95]);
axis square;

For what it's worth, see my attached random walk demos.

[Delshad Ayoubi]

Shouldn't it look more like this?

Mine looks like the one I just attached, sort of going sideways.

[Image Analyst]

I can't see the one you attached. Attach a .PNG screenshot instead. The code I gave you does produce an image like in the link you shared.

Why do you think it doesn't?

[Delshad Ayoubi]

Hmm... Maybe I'm thinking wrongly but it looks like it goes sideways instead of "up", "down" etc.

[Image Analyst]

If you limit the steps to EITHER the x direction of the y direction, but NOT BOTH, then the grid would be sideways. However, if you require that BOTH x and y change by 1, then it will look like it does. If you don't want that, then just change ONE of them, not both simultaneously. See the code below:

clc;
clearvars;

N = 100; % Length of the x-axis, also known as the length of the random walks.
M = 400; % The amount of random walks.
x_t(1) = 0;
y_t(1) = 0;

for m=1:M
  for n = 1:N % Looping all values of N into x_t(n).
    A = sign(randn); % Generates either +1/-1 depending on the SIGN of RAND.
    if rand > 0.5
      % Change only x.
      x_t(n+1) = x_t(n) + A;
      y_t(n+1) = y_t(n);
    else
      % Change only y.
      x_t(n+1) = x_t(n);
      y_t(n+1) = y_t(n) + A;
    end
  end
  plot(x_t, y_t, 'LineWidth', 2);
  hold on
end
grid on;
% Enlarge figure to full screen.
set(gcf, 'Units', 'Normalized', 'Outerposition', [0, 0.05, 1, 0.95]);
axis square;

[Delshad Ayoubi]

Alright.

How do plot the position of all the particles? I tried using 'Markersize' but it doesn't seem to make them larger.

[Delshad Ayoubi]

I created a circle using linspace. How can I create code that makes all randomwalks stay within this circle? Assuming they reach the circles surface they, with the help of IF, changes to the opposite direction instead of going through the circle.

I tried making IF statement in the For-loop but they keep going through it.

[Image Analyst]

Not hard. See if you can do it yourself. Just get the distance of the current point from the origin and keep trying while the distance > radius.

distance = sqrt(x_t(n+1)^2 + y_t(n+1)^2);
while distance > radius
    % Get new trial x_t and y_t
    x_t(n+1) = .......... etc.
    % Compute distance again with new values.
    distance = sqrt(x_t(n+1)^2 + y_t(n+1)^2);
end

Anyway, you're a smart engineer so I'm sure you can figure it out yourself without me telling you.

[Image Analyst]

Alright, seems like you're having trouble, so here is the complete code:

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.
format long g;
format compact;
fontSize = 20;

clc;
clearvars;

stepsPerWalk = 100; % Length of the x-axis, also known as the length of the random walks.
numberOfWalks = 400; % The amount of random walks.
x_t(1) = 0;
y_t(1) = 0;

% Plot a circle
radius = 20;
pos = [-radius, -radius, 2*radius, 2*radius]; 
rectangle('Position',pos,'Curvature',[1 1], 'LineWidth', 3)
axis equal;
ax = gca;
ax.FontWeight = 'bold';
ax.FontSize = 20;
ax.XAxisLocation = 'origin';
ax.YAxisLocation = 'origin';
hold on;
% Enlarge figure to full screen.
set(gcf, 'Units', 'Normalized', 'Outerposition', [0, 0.05, 1, 0.95]);

% Do the random walk.
for m = 1 : numberOfWalks
  for n = 1 : stepsPerWalk % Looping all values of N into x_t(n).
    A = sign(randn); % Generates either +1/-1 depending on the SIGN of RAND.
    if rand > 0.5
      % Change only x.
      x_t(n+1) = x_t(n) + A;
      y_t(n+1) = y_t(n);
    else
      % Change only y.
      x_t(n+1) = x_t(n);
      y_t(n+1) = y_t(n) + A;
    end
    distance = sqrt(x_t(n+1)^2 + y_t(n+1)^2);
    while distance > radius
      % Get new trial x_t and y_t
      A = sign(randn); % Generates either +1/-1 depending on the SIGN of RAND.
      if rand > 0.5
        % Change only x.
        x_t(n+1) = x_t(n) + A;
        y_t(n+1) = y_t(n);
      else
        % Change only y.
        x_t(n+1) = x_t(n);
        y_t(n+1) = y_t(n) + A;
      end
      % Compute distance again with new values.
      distance = sqrt(x_t(n+1)^2 + y_t(n+1)^2);
    end
  end
  plot(x_t, y_t, 'LineWidth', 2);
  caption = sprintf('Walk #%d of %d', m, numberOfWalks);
  title(caption, 'FontSize', 25, 'FontWeight', 'bold');
  hold on
  drawnow;
end
grid on;
% Enlarge figure to full screen.
set(gcf, 'Units', 'Normalized', 'Outerposition', [0, 0.05, 1, 0.95]);
axis square;

[Delshad Ayoubi]

How can I plot the number of random walks and then see the steps they ALL take simultaneously? As it is now, my script plots the movement of one particle to N steps, then it takes another particle and continues this way M times. How can I immediately start with M particles active and see them take N steps instead of one by one?

[Yo Seol]

How would you do a 3D random walk with the code above?

[Image Analyst]

Just add a z variable and use plot3().

[Andy Paulo Ureña]

Hi, how can i calculate the distance from the origin to all points taken in every step iteration? Thanks a lot

[Image Analyst]

@Andy Paulo Ureña make a new array called allDistances, and assign it distances

allDistances(n) = distance;